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Goodwill and Intangible Assets (Tables) | 6 Months Ended
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Jun. 30, 2021
Goodwill and Intangible Assets Disclosure [Abstract] |
Changes in goodwill | The following table reflects the changes in goodwill for the periods ended December 31, 2020, December 31, 2019 and March 31, 2021:
| (in thousands)
Balance at December 31, 2018 | $ | 832,521 |
Acquisitions | 11,257 |
Foreign currency translation and other adjustments | (7,135) |
Balance at December 31, 2019 | $ | 836,643 |
Foreign currency translation | 37,440 |
Balance at December 31, 2020 | $ | 874,083 |
Foreign currency translation | (18,505) |
Balance at March 31, 2021 (unaudited) | $ | 855,578 |
The following table reflects the changes in goodwill for the six months ended June 30, 2021:
| (in thousands)
Balance at December 31, 2020 | $ | 874,083 |
Foreign currency translation | (13,587) |
Balance at June 30, 2021 | $ | 860,496 |
Intangible assets | Intangible assets, net consisted of the following at December 31, 2020, December 31, 2019 and March 31, 2021:
| December 31, 2020 |  | December 31, 2019 |  |
| Gross Carrying Amount |  | Accumulated Amortization |  | Net |  | Gross Carrying Amount |  | Accumulated Amortization |  | Net |  |  |  |  |  |
| (in thousands) |  |
Developed product technologies | $ | 127,057 |  |  | $ | (119,392) |  |  | $ | 7,665 |  |  | $ | 124,792 |  |  | $ | (93,351) |  |  | $ | 31,441 |  |  |  |  |  |  |
Customer relationships | 131,045 |  |  | (111,336) |  |  | 19,709 |  |  | 126,788 |  |  | (83,545) |  |  | 43,243 |  |  |  |  |  |  |
Trademarks | 1,162 |  |  | (1,162) |  |  | — |  |  | 1,402 |  |  | (1,312) |  |  | 90 |  |  |  |  |  |  |
Total intangible assets, net | $ | 259,264 |  |  | $ | (231,890) |  |  | $ | 27,374 |  |  | $ | 252,982 |  |  | $ | (178,208) |  |  | $ | 74,774 |  |  |  |  |  |  |
Intangible asset amortization expense | Intangible asset amortization expense was as follows:
| Year Ended December 31, |  |
| 2020 |  | 2019 |  | 2018 |  |  |  |
| (in thousands) |  |
Intangible asset amortization expense | $ | 48,105 |  |  | $ | 47,289 |  |  | $ | 50,168 |  |  |  |  |
Amortization of acquired technologies included in cost of revenue relate to our subscription products as follows:
| Three Months Ended June 30, |  | Six Months Ended June 30,
| 2021 |  | 2020 |  | 2021 |  | 2020
| (in thousands)
Amortization of acquired technologies | $ | 1,037 |  |  | $ | 6,132 |  |  | $ | 3,741 |  |  | $ | 11,876 |
Estimated intangible asset amortization expense | As of December 31, 2020, we estimate aggregate intangible asset amortization expense to be as follows:
| Estimated Amortization
| (in thousands)
2021 | $ | 19,182 |
2022 | 7,637 |
2023 | 555 |
2024 | — |
2025 | — |

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