"EIT waves" are large-scale bright fronts observed propagating in the solar corona in association with coronal mass ejections (CMEs). An overview of the observed properties of large-scale wave-like fronts in the solar atmosphere (Moreton waves, EIT waves and similar phenomena observed in other wavelengths) is presented. The models proposed to explain these phenomena are reviewed. A particular emphasis is put on the recent EIT wave observations made by the STEREO (Solar-TErrestrial RElations Observatory) mission launched in October 2006. New key observational results and their implications for EIT wave models are discussed. It is concluded that no single model can account for the large variety of observed EIT wave properties. Prospects for future investigations of this complex phenomenon are outlined.