The unprecedented COVID-19 outbreak has significantly influenced our daily life, and COVID-19’s spread is inevitably associated with human mobility. Given the pandemic’s severity and extent of spread, a timely and comprehensive synthesis of the current state of research is needed to understand the pandemic’s impact on human mobility and corresponding government measures. This study examined the relevant literature published to the present (March 2023), identified research trends, and conducted a systematic review of evidence regarding transport’s response to COVID-19. We identified key research agendas and synthesized the results, examining: (1) mobility changes by transport modes analyzed regardless of government policy implementation, using empirical data and survey data; (2) the effect of diverse government interventions to reduce mobility and limit COVID-19 spread, and controversial issues on travel restriction policy effects; and (3) future research issues. The findings showed a strong relationship between the pandemic and mobility, with significant impacts on decreased overall mobility, a remarkable drop in transit ridership, changes in travel behavior, and improved traffic safety. Government implemented various non-pharmaceutical countermeasures, such as city lockdowns, travel restrictions, and social distancing. Many studies showed such interventions were effective. However, some researchers reported inconsistent outcomes. This review provides urban and transport planners with valuable insights to facilitate better preparation for future health emergencies that affect transportation.