The InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission landed in Elysium Planitia on Mars on 26 November 2018 and fully deployed its seismometer by the end of February 2019. The mission aims to detect, characterize and locate seismic activity on Mars, and to further constrain the internal structure, composition and dynamics of the planet. Here, we present seismometer data recorded until 30 September 2019, which reveal that Mars is seismically active. We identify 174 marsquakes, comprising two distinct populations: 150 small-magnitude, high-frequency events with waves propagating at crustal depths and 24 low-frequency, subcrustal events of magnitude M_w 3–4 with waves propagating at various depths in the mantle. These marsquakes have spectral characteristics similar to the seismicity observed on the Earth and Moon. We determine that two of the largest detected marsquakes were located near the Cerberus Fossae fracture system. From the recorded seismicity, we constrain attenuation in the crust and mantle, and find indications of a potential low-S-wave-velocity layer in the upper mantle.