Segment Information (Details) - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2016
Segment Reporting Information [Line Items]
Revenues	$ 693,747	$ 786,986	$ 691,867	$ 577,509	$ 649,385	$ 714,505	$ 622,224	$ 550,515	$ 2,750,109	$ 2,536,629	$ 2,252,422
Direct operating costs									1,556,483	1,488,406	1,356,250
Salaries and benefits									394,744	360,432	310,787
Selling, general and administrative									211,944	216,807	190,302
Goodwill and Intangible Asset Impairment									0	7,049	34,056	$ 34,056
Impairment of Intangible Assets, Finite-lived									0	7,049	2,300
Depreciation and amortization									111,744	106,021	95,030
Total operating expenses									2,274,915	2,178,715	1,986,425
Operating income	107,213	$ 193,990	$ 117,897	$ 56,094	71,160	$ 150,913	$ 90,369	$ 45,472	475,194	357,914	265,997
Interest income									1,969	1,320	2,443
Interest expense									(36,237)	(37,573)	(32,571)
Income from unconsolidated affiliates									0	(117)	48
Gain (Loss) on Extinguishment of Debt										0
Foreign currency exchange (loss) gain, net									2,701	(26,655)	20,300
Other gains									(9,820)	27	118
Other expense, net									(41,387)	(62,998)	(9,662)
Income before income taxes									433,807	294,916	256,335
Property and Equipment, net	359,980				291,869				359,980	291,869	268,303
Total Assets	4,657,666				3,321,155				4,657,666	3,321,155	3,140,029
Eft Processing Segment [Member]
Segment Reporting Information [Line Items]
Revenues									888,712	753,651	634,559
Direct operating costs									397,132	366,977	318,875
Salaries and benefits									87,603	75,791	61,683
Selling, general and administrative									35,518	46,925	33,158
Goodwill and Intangible Asset Impairment									0	0		2,286
Depreciation and amortization									71,819	66,713	55,660
Total operating expenses									592,072	556,406	471,662
Operating income									296,640	197,245	162,897
Property and Equipment, net	266,872				215,106				266,872	215,106	196,451
Total Assets	1,914,144				1,220,141				1,914,144	1,220,141	1,040,135
Epay Segment [Member]
Segment Reporting Information [Line Items]
Revenues									769,329	743,784	733,998
Direct operating costs									576,757	564,252	564,032
Salaries and benefits									61,540	57,748	54,459
Selling, general and administrative									35,054	35,749	36,014
Goodwill and Intangible Asset Impairment									0	0		31,770
Depreciation and amortization									6,774	7,038	9,622
Total operating expenses									680,125	664,787	695,897
Operating income									89,204	78,997	38,101
Property and Equipment, net	41,539				31,172				41,539	31,172	28,135
Total Assets	962,671				780,220				962,671	780,220	695,990
Money Transfer Segment [Member]
Segment Reporting Information [Line Items]
Revenues									1,096,226	1,042,962	886,858
Direct operating costs									586,730	560,930	476,322
Salaries and benefits									208,792	194,808	168,371
Selling, general and administrative									133,068	125,647	108,022
Goodwill and Intangible Asset Impairment										7,049		0
Impairment of Intangible Assets, Finite-lived									0
Depreciation and amortization									32,846	32,002	29,598
Total operating expenses									961,436	920,436	782,313
Operating income									134,790	122,526	104,545
Property and Equipment, net	51,519				45,517				51,519	45,517	43,564
Total Assets	1,560,136				1,310,775				1,560,136	1,310,775	1,255,765
Unallocated Amount to Segment, Intersegment Eliminations and Other [Member]
Segment Reporting Information [Line Items]
Revenues									(4,158)	(3,768)	(2,993)
Direct operating costs									(4,136)	(3,753)	(2,979)
Salaries and benefits									36,809	32,085	26,274
Selling, general and administrative									8,304	8,486	13,108
Goodwill and Intangible Asset Impairment									0	0		$ 0
Depreciation and amortization									305	268	150
Total operating expenses									41,282	37,086	36,553
Operating income									(45,440)	(40,854)	(39,546)
Property and Equipment, net	50				74				50	74	153
Total Assets	220,715				10,019				220,715	10,019	148,139
UNITED STATES
Segment Reporting Information [Line Items]
Revenues									716,576	721,977	572,383
Property and Equipment, net	49,904				29,499				49,904	29,499
Total Assets	717,894				493,428				717,894	493,428
Non-US [Member]
Segment Reporting Information [Line Items]
Revenues									2,033,533	1,814,652	1,680,039
Property and Equipment, net	310,076				262,370				310,076	262,370
Total Assets	3,939,772				2,827,727				3,939,772	2,827,727
AUSTRALIA
Segment Reporting Information [Line Items]
Revenues									51,686	58,039	77,777
Property and Equipment, net	1,992				2,051				1,992	2,051
Total Assets	62,844				61,215				62,844	61,215
GREECE
Segment Reporting Information [Line Items]
Revenues									79,716	71,007	71,197
Property and Equipment, net	11,753				11,267				11,753	11,267
Total Assets	111,339				58,419				111,339	58,419
UNITED KINGDOM
Segment Reporting Information [Line Items]
Revenues									135,006	133,132	136,977
Property and Equipment, net	22,420				20,525				22,420	20,525
Total Assets	520,549				519,918				520,549	519,918
GERMANY
Segment Reporting Information [Line Items]
Revenues									518,146	476,122	495,778
Property and Equipment, net	35,824				25,302				35,824	25,302
Total Assets	660,730				508,062				660,730	508,062
POLAND
Segment Reporting Information [Line Items]
Revenues									130,104	126,513	128,672
Property and Equipment, net	42,916				50,359				42,916	50,359
Total Assets	222,582				155,821				222,582	155,821
SPAIN
Segment Reporting Information [Line Items]
Revenues									189,104	155,619	115,473
Property and Equipment, net	55,240				39,238				55,240	39,238
Total Assets	371,882				198,082				371,882	198,082
NEW ZEALAND
Segment Reporting Information [Line Items]
Revenues									47,611	48,881	47,091
Property and Equipment, net	3,137				2,718				3,137	2,718
Total Assets	237,076				196,869				237,076	196,869
Other countries [Member]
Segment Reporting Information [Line Items]
Revenues									468,785	397,334	323,095
ITALY
Segment Reporting Information [Line Items]
Revenues									130,929	103,691	89,276
Property and Equipment, net	20,663				15,238				20,663	15,238
Total Assets	210,910				157,314				210,910	157,314
MALAYSIA
Segment Reporting Information [Line Items]
Revenues									74,948	76,380	56,287
Property and Equipment, net	2,629				2,802				2,629	2,802
Total Assets	114,796				103,043				114,796	103,043
FRANCE
Segment Reporting Information [Line Items]
Revenues									94,352	75,466	56,027
Property and Equipment, net	1,508				1,037				1,508	1,037
Total Assets	96,636				76,687				96,636	76,687
INDIA
Segment Reporting Information [Line Items]
Revenues									113,146	92,468	82,389
Property and Equipment, net	27,281				19,554				27,281	19,554
Total Assets	163,125				89,923				163,125	89,923
Other geographic locations [Member]
Segment Reporting Information [Line Items]
Revenues									41,917	33,696	27,949
Property and Equipment, net	84,713				72,279				84,713	72,279
Total Assets	$ 1,167,303				$ 702,374				1,167,303	702,374
Other geographic locations [Member] | Eft Processing Segment [Member]
Segment Reporting Information [Line Items]
Revenues									28	58	142
Other geographic locations [Member] | Epay Segment [Member]
Segment Reporting Information [Line Items]
Revenues									16,915	15,330	18,102
Other geographic locations [Member] | Money Transfer Segment [Member]
Segment Reporting Information [Line Items]
Revenues									$ 24,974	$ 18,308	$ 9,705