Income Taxes - Narrative (Details) € in Thousands, $ in Thousands		1 Months Ended			12 Months Ended			72 Months Ended
	Nov. 23, 2022 EUR (€)	Apr. 30, 2022 EUR (€)	Jun. 30, 2021 EUR (€)	Dec. 31, 2020 EUR (€)	Dec. 31, 2022 USD ($)	Dec. 31, 2021 USD ($)	Dec. 31, 2020 USD ($)	Dec. 31, 2010 EUR (€)
Income Taxes [Line Items]
Valuation allowance against deferred tax asset					$ 284,347	$ 236,357
Increase (decrease) in the valuation allowance					47,990	(31,481)
Net operating loss carryforwards and tax credit					448,759	408,434
Net operating loss carryforwards in the U.S.					6,753
Net operating loss carryforwards in various foreign jurisdictions					1,565,514
Gross unrecognized tax benefits					1,230,632	1,296,523	$ 1,388,391
Unrecognized tax benefits that would impact effective tax rate					47,881
Interest and penalties					14,801	14,494
Accrued/(reversed) interest and penalties					437	$ 3,236	$ (695)
Expected decrease in unrecognized tax benefits within next twelve months					9,152
Luxembourg
Income Taxes [Line Items]
Net operating loss carryforwards in various foreign jurisdictions					$ 1,169,896
Domestic tax authority
Income Taxes [Line Items]
Effective income tax rate (as a percent)					(36.50%)	33.80%	(12.00%)
Foreign tax authority
Income Taxes [Line Items]
Effective income tax rate (as a percent)					17.50%	14.10%	16.30%
Foreign tax authority | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €	€ 3,000
Foreign tax authority | Tax Years 2005 to 2010 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €								€ 223,321
Foreign tax authority | Tax Year 2018 | Luxembourg
Income Taxes [Line Items]
Foreign tax assessment | €			€ 371,696	€ 371,696
Foreign tax authority | Tax Year 2018 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €		€ 186,734
State
Income Taxes [Line Items]
Net operating loss carryforwards and tax credit					$ 46,388
State deferred tax assets
Income Taxes [Line Items]
Valuation allowance against deferred tax asset					31,760
Operating Loss Carryforward, Domestic
Income Taxes [Line Items]
Valuation allowance against deferred tax asset					6,242
Operating Loss Carryforward, Foreign Jurisdiction
Income Taxes [Line Items]
Valuation allowance against deferred tax asset					$ 246,345