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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 |  |  |

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