Brazil is an epicentre for COVID-19 in Latin America. In this report we describe the Brazilian epidemic using three epidemiological measures: the number of infections, the number of deaths and the reproduction number. Our modelling framework requires sufficient death data to estimate trends, and we therefore limit our analysis to 16 states that have experienced a total of more than fifty deaths. The distribution of deaths among states is highly heterogeneous, with 5 states—Sao Paulo, Rio de Janeiro, Ceara, Pernambuco and Amazonas—accounting for 81% of deaths reported to date. In these states, we estimate that the percentage of people that have been infected with SARS-CoV-2 ranges from 3.3% (95% CI: 2.8%-3.7%) in Sao Paulo to 10.6% (95% CI: 8.8%-12.1%) in Amazonas. The reproduction number (a measure of transmission intensity) at the start of the epidemic meant that an infected individual would infect three or four others on average. Following non-pharmaceutical interventions such as school closures and decreases in population mobility, we show that the reproduction number has dropped substantially in each state. However, for all 16 states we study, we estimate with high confidence that the reproduction number remains above 1. A reproduction number above 1 means that the epidemic is not yet controlled and will continue to grow. These trends are in stark contrast to other major COVID-19 epidemics in Europe and Asia where enforced lockdowns have successfully driven the reproduction number below 1. While the Brazilian epidemic is still relatively nascent on a national scale, our results suggest that further action is needed to limit spread and prevent health system overload.