Earth observation (EO) satellite missions have been providing detailed images about the state of Earth and its land cover for over 50 years. Long-term missions, such as those of NASA's Landsat, Terra, and Aqua satellites, and more recently, the European Space Agency's (ESA's) Sentinel missions, record images of the entire world every few days. Although single images provide point-in-time data, repeated images of the same area, or satellite image time series (SITS), provide information about the changing state of vegetation and land use. These SITS are useful for modeling dynamic processes and seasonal changes, such as plant phenology. They have potential benefits for many aspects of land and natural resource management, including applications in agricultural, forest, water, and disaster management; urban planning; and mining. However, the resulting SITS are complex, incorporating information from the temporal, spatial, and spectral dimensions. Therefore, deep learning (DL) methods are often deployed, as they can analyze these complex relationships. This review article presents a summary of the state-of-the-art methods of modeling environmental, agricultural, and other EO variables from SITS data using DL methods. We aim to provide a resource for remote sensing experts interested in using DL techniques to enhance EO models with temporal information.