<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>106 - Disclosure - The Company and Basis of Presentation</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>eol_PE694307--1310-Q0005_STD_181_20130630_0</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001344413</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="Jun. 30, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>us-gaap_AccountingPoliciesAbstract</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Accounting Policies [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="eol_PE694307--1310-Q0005_STD_181_20130630_0" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div&gt;
&lt;p style="MARGIN-TOP: 12px; MARGIN-BOTTOM: 0px"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&lt;b&gt;1. The Company and Basis
of Presentation&lt;/b&gt;&lt;/font&gt;&lt;/p&gt;
&lt;!-- xbrl,body --&gt;
&lt;p style="MARGIN-TOP: 6px; MARGIN-BOTTOM: 0px"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&lt;b&gt;Business&lt;/b&gt;&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 6px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Alexza
Pharmaceuticals, Inc. (the &amp;#x201C;Company&amp;#x201D;), was incorporated
in the state of Delaware on December&amp;#xA0;19, 2000 as FaxMed, Inc.
In June 2001, the Company changed its name to Alexza Corporation
and in December 2001 became Alexza Molecular Delivery Corporation.
In July 2005, the Company changed its name to Alexza
Pharmaceuticals, Inc.&lt;/font&gt;&lt;/p&gt;
&lt;p style="PADDING-BOTTOM: 0px; MARGIN-TOP: 12px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;The Company is
a pharmaceutical development company focused on the research,
development, and commercialization of novel proprietary products
for the acute treatment of central nervous system conditions. The
Company&amp;#x2019;s first commercial product, ADASUVE&lt;font style="FONT-FAMILY: Times New Roman" size="1"&gt;&lt;sup style="POSITION: relative; BOTTOM: 0.8ex; VERTICAL-ALIGN: baseline"&gt;&amp;#xAE;&lt;/sup&gt;&lt;/font&gt;,
or Staccato&lt;font style="FONT-FAMILY: Times New Roman" size="1"&gt;&lt;sup style="POSITION: relative; BOTTOM: 0.8ex; VERTICAL-ALIGN: baseline"&gt;&amp;#xAE;&lt;/sup&gt;&lt;/font&gt;
loxapine, and its product candidates are all based on the
&lt;i&gt;Staccato&lt;/i&gt; system, a proprietary technology developed by the
Company. The Company&amp;#x2019;s facilities and employees are currently
located in the United States, and the Company operates in one
business segment.&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;In May 2013,
the Company entered into a License and Supply Agreement (the
&amp;#x201C;Teva Agreement&amp;#x201D;) with Teva Pharmaceuticals USA, Inc.
(&amp;#x201C;Teva&amp;#x201D;) to provide Teva with an exclusive license to
develop and commercialize ADASUVE in the U.S. (see Note 10). The
Company has an existing Collaboration, License and Supply Agreement
(the &amp;#x201C;Ferrer Agreement&amp;#x201D;) with Grupo Ferrer
Internacional, S.A. (&amp;#x201C;Ferrer&amp;#x201D;) for the
commercialization of ADASUVE in Europe, Latin American, Russia and
the Commonwealth of Independent States countries (see Note
10).&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 18px; MARGIN-BOTTOM: 0px"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&lt;b&gt;Basis of
Presentation&lt;/b&gt;&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 6px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;The
accompanying unaudited condensed consolidated financial statements
have been prepared in accordance with accounting principles
generally accepted in the United States of America for interim
financial information and with the instructions to Form 10-Q and
Rule 8-03 of Regulation S-X. Accordingly, they do not contain all
of the information and footnotes required for complete financial
statements. In the opinion of management, the accompanying
unaudited condensed consolidated financial statements reflect all
adjustments, which include only normal recurring adjustments,
necessary to present fairly the Company&amp;#x2019;s interim
consolidated financial information. The results for the three and
six months ended June&amp;#xA0;30, 2013 are not necessarily indicative
of the results to be expected for the year ending December&amp;#xA0;31,
2013 or for any other interim period or any other future
year.&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;The
accompanying unaudited condensed consolidated financial statements
and notes to condensed consolidated financial statements should be
read in conjunction with the audited consolidated financial
statements for the year ended December&amp;#xA0;31, 2012 included in
the Company&amp;#x2019;s Annual Report on Form 10-K filed with the
Securities and Exchange Commission (&amp;#x201C;SEC&amp;#x201D;) on
March&amp;#xA0;26, 2013.&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 18px; MARGIN-BOTTOM: 0px"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&lt;b&gt;Basis of
Consolidation&lt;/b&gt;&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 6px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;The unaudited
condensed consolidated financial statements include the accounts of
the Company and its wholly-owned subsidiaries. All significant
intercompany balances and transactions have been
eliminated.&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 18px; MARGIN-BOTTOM: 0px"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&lt;b&gt;Significant Risks and
Uncertainties&lt;/b&gt;&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 6px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;The Company has
incurred significant losses from operations since its inception and
expects losses to continue for the foreseeable future. As of
June&amp;#xA0;30, 2013, the Company had cash, cash equivalents and
marketable securities of $35.0 million and working capital of $20.9
million. The Company believes that, based on its cash, cash
equivalents and marketable securities balance at June&amp;#xA0;30,
2013, estimated product revenues and royalties associated with the
sale of ADASUVE, proceeds available under the Convertible
Promissory Note and Agreement to Lend with Teva (the &amp;#x201C;Teva
Note&amp;#x201D;, see Note 8) and its current expected cash usage, it
has sufficient capital resources to meet its anticipated cash needs
into the third quarter of 2014. The Company plans to raise
additional capital to fund its operations and working capital, to
develop its product candidates and to continue the development of
its commercial manufacturing capabilities. In addition to product
revenues, royalties and milestone payments, the Company plans to
finance its operations through the sale of equity securities,
utilization of debt arrangements, such as the Teva Note (see Note
8), or additional distribution or licensing collaborations. Such
funding may not be available or may be on terms that are not
favorable to the Company. The Company&amp;#x2019;s inability to raise
capital as and when needed could have a negative impact on its
financial condition and its ability to continue as a going concern.
The accompanying financial statements have been prepared assuming
the Company will continue to operate as a going concern, which
contemplates the realization of assets and the settlement of
liabilities in the normal course of business. The consolidated
financial statements do not include any adjustments to reflect the
possible future effects on the recoverability and classification of
assets or the amounts of liabilities that may result from
uncertainty related to the Company&amp;#x2019;s ability to continue as a
going concern.&lt;/font&gt;&lt;/p&gt;
&lt;/div&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>The entire disclosure for organization, consolidation and basis of presentation of financial statements disclosure.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 810

 -SubTopic 10

 -Section 50

 -Paragraph 8

 -URI http://asc.fasb.org/extlink&amp;oid=28200181&amp;loc=SL6228881-111685



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 720

 -SubTopic 15

 -URI http://asc.fasb.org/subtopic&amp;trid=2122524



Reference 3: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 205

 -SubTopic 10

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=6359566&amp;loc=d3e326-107755



Reference 4: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 235

 -SubTopic 10

 -Section 50

 -Paragraph 3

 -URI http://asc.fasb.org/extlink&amp;oid=6367646&amp;loc=d3e18780-107790



Reference 5: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 205

 -SubTopic 10

 -Section 45

 -Paragraph 3

 -URI http://asc.fasb.org/extlink&amp;oid=7668296&amp;loc=d3e288-107754



Reference 6: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 810

 -SubTopic 10

 -URI http://asc.fasb.org/subtopic&amp;trid=2197480



Reference 7: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 810

 -SubTopic 10

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=18733093&amp;loc=d3e5614-111684



Reference 8: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 915

 -SubTopic 235

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=6472506&amp;loc=d3e38932-110933



Reference 9: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 852

 -SubTopic 10

 -URI http://asc.fasb.org/subtopic&amp;trid=2209116



Reference 10: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 272

 -SubTopic 10

 -Section 50

 -Paragraph 3

 -URI http://asc.fasb.org/extlink&amp;oid=6373374&amp;loc=d3e70478-108055



Reference 11: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 275

 -SubTopic 10

 -URI http://asc.fasb.org/subtopic&amp;trid=2134480



Reference 12: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 205

 -SubTopic 10

 -URI http://asc.fasb.org/subtopic&amp;trid=2122150



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>The Company and Basis of Presentation</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>The Company and Basis of Presentation</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.alexza.com/taxonomy/role/NotesToFinancialStatementsOrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
