NASA’s InSight (Interior exploration using Seismic Investigations, Geodesy and Heat Transport) mission landed in Elysium Planitia on Mars on 26 November 2018. It aims to determine the interior structure, composition and thermal state of Mars, as well as constrain present-day seismicity and impact cratering rates. Such information is key to understanding the differentiation and subsequent thermal evolution of Mars, and thus the forces that shape the planet’s surface geology and volatile processes. Here we report an overview of the first ten months of geophysical observations by InSight. As of 30 September 2019, 174 seismic events have been recorded by the lander’s seismometer, including over 20 events of moment magnitude Mw = 3–4. The detections thus far are consistent with tectonic origins, with no impact-induced seismicity yet observed, and indicate a seismically active planet. An assessment of these detections suggests that the frequency of global seismic events below approximately Mw = 3 is similar to that of terrestrial intraplate seismic activity, but there are fewer larger quakes; no quakes exceeding Mw = 4 have been observed. The lander’s other instruments—two cameras, atmospheric pressure, temperature and wind sensors, a magnetometer and a radiometer—have yielded much more than the intended supporting data for seismometer noise characterization: magnetic field measurements indicate a local magnetic field that is ten-times stronger than orbital estimates and meteorological measurements reveal a more dynamic atmosphere than expected, hosting baroclinic and gravity waves and convective vortices. With the mission due to last for an entire Martian year or longer, these results will be built on by further measurements by the InSight lander.