During the COVID-19 pandemic, many countries imposed mobility restrictions to reduce transmission and control the spread of the disease. Anonymised and aggregated mobile operator data, such as call detail records (CDRs), can provide near-real time insights into population mobility with high spatial and temporal resolution, across a whole country. Such data are useful for monitoring the impact of these restrictions on mobility and therefore help assess their potential impact on the spread of COVID-19. Flowminder supported the global response to the COVID-19 pandemic by working with mobile network operators, governments, and development actors, throughout 2020-2021 to rapidly generate CDR-derived insights related to population distribution and mobility changes caused by the pandemic and the associated mobility restrictions in seven countries (Curacao, the Democratic Republic of the Congo (DRC), Ghana, Haiti, Namibia, Papua New Guinea, and Sierra Leone). Here, we detail the key analyses conducted to assess the impact of the response to the pandemic and mobility restrictions on mobility and the key learnings on rapid analysis of fast varying mobility indicators in multiple countries.