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Income Taxes - Narrative (Details) € in Thousands, $ in Thousands | 1 Months Ended | 12 Months Ended | 72 Months Ended
--- | --- | --- | ---
Dec. 31, 2021 EUR (€) | Jun. 30, 2021 EUR (€) | Dec. 31, 2021 USD ($) | Dec. 31, 2020 USD ($) | Dec. 31, 2019 USD ($) | Dec. 31, 2010 EUR (€)
Income Taxes [Line Items] |  |  |  |  |  |
Percentage of earnings from continuing operations before income taxes attributable to the United States (as a percent) |  |  | 30.00% |  |  |
Valuation allowance against deferred tax asset |  |  | $ 236,357 | $ 267,838 |  |
Increase (decrease) in the valuation allowance |  |  | (31,481) | 35,642 |  |
Net operating loss carryforwards and tax credit |  |  | 408,434 | 433,822 |  |
Net operating loss carryforwards in the U.S. |  |  | 6,173 |  |  |
Net operating loss carryforwards in various foreign jurisdictions |  |  | 1,596,351 |  |  |
Gross unrecognized tax benefits |  |  | 1,296,523 | 1,388,391 | $ 1,260,970 |
Unrecognized tax benefits that would impact effective tax rate |  |  | 45,147 |  |  |
Interest and penalties |  |  | 14,494 | 11,485 |  |
Accrued/(reversed) interest and penalties |  |  | 3,236 | $ (695) | 5,368 |
Expected decrease in unrecognized tax benefits within next twelve months |  |  | $ 19,510 |  |  |
Luxembourg |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |
Net operating loss carryforwards in various foreign jurisdictions |  |  |  |  | $ 1,238,277 |
Domestic tax authority |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |
Effective income tax rate (as a percent) |  |  | 33.80% | (12.00%) | 36.60% |
Foreign tax authority |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |
Effective income tax rate (as a percent) |  |  | 14.10% | 16.30% | (9.40%) |
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 | € | € 182,594 | € 371,696 |  |  |  |
State |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |
Net operating loss carryforwards and tax credit |  |  | $ 44,186 |  |  |
State deferred tax assets |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |
Valuation allowance against deferred tax asset |  |  | 22,851 |  |  |
Operating Loss Carryforward, Domestic |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |
Valuation allowance against deferred tax asset |  |  | 5,882 |  |  |
Operating Loss Carryforward, Foreign Jurisdiction |  |  |  |  |  |
Income Taxes [Line Items] |  |  |  |  |  |
Valuation allowance against deferred tax asset |  |  | $ 207,624 |  |  |

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