Income Taxes - Narrative (Details) € in Thousands, $ in Thousands				12 Months Ended			36 Months Ended
	Dec. 22, 2020 EUR (€)	Oct. 22, 2020 EUR (€)	Mar. 10, 2020 EUR (€)	Dec. 31, 2020 USD ($)	Dec. 31, 2019 USD ($)	Dec. 31, 2018 USD ($)	Dec. 31, 2014 EUR (€)
Income Taxes [Line Items]
Percentage of earnings from continuing operations before income taxes attributable to the United States				16.00%
Valuation allowance against deferred tax asset				$ 267,838	$ 232,196
Increase (decrease) in the valuation allowance				35,642	(115,590)
Net operating loss carryforwards and tax credit				433,822	376,375
Net operating loss carryforwards in the U.S.				10,179
Net operating loss carryforwards in various foreign jurisdictions				1,710,619
Repatriation transition tax expense					134,754
Accumulated earnings					2,126,617
Distribution of previously taxed earnings				1,742,539
Gross unrecognized tax benefits				1,388,391	1,260,970	$ 1,330,713
Unrecognized tax benefits that would impact effective tax rate				33,144
Interest and penalties				11,485	12,555
Accrued/(reversed) interest and penalties				(695)	5,368	$ (1,085)
Expected decrease in unrecognized tax benefits within next twelve months				$ 8,575
Luxembourg
Income Taxes [Line Items]
Net operating loss carryforwards in various foreign jurisdictions					$ 1,344,589
Domestic tax authority
Income Taxes [Line Items]
Effective income tax rate				(12.00%)	36.60%	28.70%
Foreign tax authority
Income Taxes [Line Items]
Effective income tax rate				16.30%	(9.40%)	11.00%
Foreign tax authority | Tax year 2005 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €							€ 46,135
Foreign tax authority | Tax year 2006 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €							38,817
Foreign tax authority | Tax year 2007 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €							39,635
Foreign tax authority | Tax year 2008 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €							30,131
Foreign tax authority | Tax year 2009 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €							25,486
Foreign tax authority | Tax year 2010 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €							€ 43,117
Foreign tax authority | Tax Year 2016 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €			€ 67,959
Foreign tax authority | Tax year 2017 | Luxembourg
Income Taxes [Line Items]
Foreign tax assessment | €		€ 65,152
Foreign tax authority | Tax year 2017 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €	€ 17,655
Foreign tax authority | Tax year 2013 | Luxembourg
Income Taxes [Line Items]
Foreign tax assessment | €		€ 45,466
State
Income Taxes [Line Items]
Net operating loss carryforwards and tax credit				$ 57,613
Tax Rate Changes, Foreign Currency Translations, and Other Activities
Income Taxes [Line Items]
Increase (decrease) in the valuation allowance					$ 32,650
State deferred tax assets
Income Taxes [Line Items]
Valuation allowance against deferred tax asset				29,919
Operating Loss Carryforward, Domestic
Income Taxes [Line Items]
Valuation allowance against deferred tax asset				5,881
Operating Loss Carryforward, Foreign Jurisdiction
Income Taxes [Line Items]
Valuation allowance against deferred tax asset				$ 232,038
Restructuring Charges
Income Taxes [Line Items]
Increase (decrease) in the valuation allowance					$ 148,240