Segment Information (Details) - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2017	Sep. 30, 2017	Jun. 30, 2017	Mar. 31, 2017	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2016
Segment Reporting Information [Line Items]
Revenues	$ 649,385	$ 714,505	$ 622,224	$ 550,515	$ 604,645	$ 637,834	$ 536,563	$ 473,380	$ 2,536,629	$ 2,252,422	$ 1,958,615
Direct operating costs									1,488,406	1,356,250	1,174,545
Salaries and benefits									360,432	310,787	288,420
Selling, general and administrative									216,807	190,302	165,348
Goodwill and Intangible Asset Impairment									7,049	34,056	0
Depreciation and amortization									106,021	95,030	80,529
Total operating expenses									2,178,715	1,986,425	1,708,842
Operating income	71,160	$ 150,913	$ 90,369	$ 45,472	41,119	$ 116,901	$ 66,691	$ 41,286	357,914	265,997	249,773
Interest income									1,320	2,443	1,696
Interest expense									(37,573)	(32,571)	(28,332)
Income from unconsolidated affiliates									(117)	48	0
Foreign currency exchange (loss) gain, net									(26,655)	20,300	(10,200)
Other gains									27	118	19,956
Other expense, net									(62,998)	(9,662)	(16,880)
Income before income taxes									294,916	256,335	232,893
Property and Equipment, net	291,869				268,303				291,869	268,303	202,145
Total Assets	3,321,155				3,140,029				3,321,155	3,140,029	2,712,872
Eft Processing Segment [Member]
Segment Reporting Information [Line Items]
Revenues									753,651	634,559	464,254
Direct operating costs									366,977	318,875	224,793
Salaries and benefits									75,791	61,683	51,822
Selling, general and administrative									46,925	33,158	30,399
Goodwill and Intangible Asset Impairment									0	2,286
Depreciation and amortization									66,713	55,660	40,084
Total operating expenses									556,406	471,662	347,098
Operating income									197,245	162,897	117,156
Property and Equipment, net	215,106				196,451				215,106	196,451	139,161
Total Assets	1,220,141				1,040,135				1,220,141	1,040,135	786,166
Epay Segment [Member]
Segment Reporting Information [Line Items]
Revenues									743,784	733,998	693,986
Direct operating costs									564,252	564,032	528,774
Salaries and benefits									57,748	54,459	51,378
Selling, general and administrative									35,749	36,014	34,517
Goodwill and Intangible Asset Impairment									0	31,770
Depreciation and amortization									7,038	9,622	11,075
Total operating expenses									664,787	695,897	625,744
Operating income									78,997	38,101	68,242
Property and Equipment, net	31,172				28,135				31,172	28,135	23,939
Total Assets	780,220				695,990				780,220	695,990	733,514
Money Transfer Segment [Member]
Segment Reporting Information [Line Items]
Revenues									1,042,962	886,858	801,919
Direct operating costs									560,930	476,322	422,508
Salaries and benefits									194,808	168,371	155,471
Selling, general and administrative									125,647	108,022	93,219
Goodwill and Intangible Asset Impairment									7,049	0
Depreciation and amortization									32,002	29,598	29,195
Total operating expenses									920,436	782,313	700,393
Operating income									122,526	104,545	101,526
Property and Equipment, net	45,517				43,564				45,517	43,564	38,954
Total Assets	1,310,775				1,255,765				1,310,775	1,255,765	1,136,722
Unallocated Amount to Segment, Intersegment Eliminations and Other [Member]
Segment Reporting Information [Line Items]
Revenues									(3,768)	(2,993)	(1,544)
Direct operating costs									(3,753)	(2,979)	(1,530)
Salaries and benefits									32,085	26,274	29,749
Selling, general and administrative									8,486	13,108	7,213
Goodwill and Intangible Asset Impairment									0	0
Depreciation and amortization									268	150	175
Total operating expenses									37,086	36,553	35,607
Operating income									(40,854)	(39,546)	(37,151)
Property and Equipment, net	74				153				74	153	91
Total Assets	10,019				148,139				10,019	148,139	56,470
UNITED STATES
Segment Reporting Information [Line Items]
Revenues									721,977	572,383	548,877
Property and Equipment, net	29,499				28,465				29,499	28,465
Total Assets	493,428				592,187				493,428	592,187
Non-US [Member]
Segment Reporting Information [Line Items]
Revenues									1,814,652	1,680,039	1,409,738
Property and Equipment, net	262,370				239,838				262,370	239,838
Total Assets	2,827,727				2,547,842				2,827,727	2,547,842
AUSTRALIA
Segment Reporting Information [Line Items]
Revenues									58,039	77,777	77,198
Property and Equipment, net	2,051				2,704				2,051	2,704
Total Assets	61,215				76,370				61,215	76,370
GREECE
Segment Reporting Information [Line Items]
Revenues									71,007	71,197	44,361
Property and Equipment, net	11,267				10,012				11,267	10,012
Total Assets	58,419				62,552				58,419	62,552
UNITED KINGDOM
Segment Reporting Information [Line Items]
Revenues									133,132	136,977	131,826
Property and Equipment, net	20,525				20,104				20,525	20,104
Total Assets	519,918				532,421				519,918	532,421
GERMANY
Segment Reporting Information [Line Items]
Revenues									476,122	495,778	409,590
Property and Equipment, net	25,302				20,668				25,302	20,668
Total Assets	508,062				435,687				508,062	435,687
POLAND
Segment Reporting Information [Line Items]
Revenues									126,513	128,672	115,269
Property and Equipment, net	50,359				61,636				50,359	61,636
Total Assets	155,821				176,766				155,821	176,766
SPAIN
Segment Reporting Information [Line Items]
Revenues									155,619	115,473	82,921
Property and Equipment, net	39,238				29,881				39,238	29,881
Total Assets	198,082				152,841				198,082	152,841
NEW ZEALAND
Segment Reporting Information [Line Items]
Revenues									48,881	47,091	40,890
Property and Equipment, net	2,718				2,574				2,718	2,574
Total Assets	196,869				185,459				196,869	185,459
ITALY
Segment Reporting Information [Line Items]
Revenues									103,691	89,276	72,591
Property and Equipment, net	15,238				12,078				15,238	12,078
Total Assets	157,314				123,218				157,314	123,218
MALAYSIA
Segment Reporting Information [Line Items]
Revenues									76,380	56,287	53,787
Property and Equipment, net	2,802				3,161				2,802	3,161
Total Assets	103,043				124,522				103,043	124,522
FRANCE
Segment Reporting Information [Line Items]
Revenues									75,466	56,027	43,247
Property and Equipment, net	1,037				1,104				1,037	1,104
Total Assets	76,687				65,366				76,687	65,366
INDIA
Segment Reporting Information [Line Items]
Revenues									92,468	82,389	75,243
Property and Equipment, net	19,554				13,090				19,554	13,090
Total Assets	89,923				82,513				89,923	82,513
Other geographic locations [Member]
Segment Reporting Information [Line Items]
Revenues									397,334	323,095	$ 262,815
Property and Equipment, net	72,279				62,826				72,279	62,826
Total Assets	$ 702,374				$ 530,127				$ 702,374	$ 530,127