The atmosphere of Mars is thin, although rich in dust aerosols, and covers a dry surface. As such, Mars provides an opportunity to expand our knowledge of atmospheres beyond that attainable from the atmosphere of the Earth. The InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) lander is measuring Mars’s atmosphere with unprecedented continuity, accuracy and sampling frequency. Here we show that InSight unveils new atmospheric phenomena at Mars, especially in the higher-frequency range, and extends our understanding of Mars’s meteorology at all scales. InSight is uniquely sensitive to large-scale and regional weather and obtained detailed in situ coverage of a regional dust storm on Mars. Images have enabled high-altitude wind speeds to be measured and revealed airglow—faint emissions produced by photochemical reactions—in the middle atmosphere. InSight observations show a paradox of aeolian science on Mars: despite having the largest recorded Martian vortex activity and dust-devil tracks close to the lander, no visible dust devils have been seen. Meteorological measurements have produced a catalogue of atmospheric gravity waves, which included bores (soliton-like waves). From these measurements, we have discovered Martian infrasound and unexpected similarities between atmospheric turbulence on Earth and Mars. We suggest that the observations of Mars’s atmosphere by InSight will be key for prediction capabilities and future exploration. All co-authors acknowledge NASA, CNES and its partner agencies and institutions (UKSA, SSO, DLR, JPL, IPGP-CNRS, ETHZ, IC and MPS-MPG) and the flight operations team at JPL, CAB, SISMOC, MSDS, IRIS-DMC and PDS for providing InSight data. The members of the InSight engineering and operations teams made the InSight mission possible and their hard work and dedication is acknowledged here. A portion of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Additional work was supported by NASA's InSight Participating Scientist Program. The French co-authors acknowledge the French Space Agency CNES, which funded scientific activities and supported SEIS-related contracts and CNES employees. Additional funding support was provided by Agence Nationale de la Recherche (ANR-14-CE36-0012-02 SIMARS and ANR-19-CE31-0008-08 MAGIS). Atmospheric modelling used HPC resources of CINES (Centre Informatique National de l'Enseignement Superieur) under the allocations A0040110391 and A0060110391 attributed by GENCI (Grand Equipement National de Calcul Intensif). The Spanish co-authors acknowledge funding by the Centro de Desarrollo Tecnologico e Industrial (CDTI), Ministerio de Economia y Competitividad and the Instituto Nacional de Tecnica Aeroespacial (INTA). The Swiss co-authors acknowledge funding by the Swiss National Science Foundation (SNF-ANR project 157133) and the Swiss State Secretariat for Education, Research and Innovation (SEFRI project MarsQuake Service-Preparatory Phase). The UK co-authors acknowledge funding by the UK Space Agency. This paper is InSight Contribution Number 103; With funding from the Spanish government through the "María de Maeztu Unit of Excellence" accreditation (MDM-2017-0737). Peer review