The last decade witnessed an explosion in yearly number of publications on passive glacier seismology. The seismic signals from a wide range of glacier‐related processes fill a broad band of frequencies (from 10−3 to 102 Hz) and moment magnitudes (from M–3 to M7) providing a fresh and unprecedented view on fundamental processes in the cryosphere. New insights into basal motion, iceberg calving, glacier, iceberg, and sea ice dynamics, and precursory signs of unstable glaciers and ice structural changes are being discovered with seismological techniques. These observations offer an invaluable foundation for understanding ongoing environmental changes and for future monitoring of ice bodies worldwide. In this review we discuss seismic sources in the cryosphere as well as research challenges for the near future. The field of glacier seismology is evolving so rapidly that some parts of this review will likely soon be outdated. Nevertheless, given an overwhelming number of recent publications and rapidly growing seismic data volumes provided by modern seismic installations in polar and mountain regions, this introduction to cryosphere seismicity aims to serve as a timely and comprehensive reference for glaciologists and seismologists.