Convection often produces severe weather which causes a great loss to human lives and properties. Precisely predicting the convection initiation process is crucial but challenging in operational convection nowcasting (0~2 h forecasting). Before the radar-defined CI occurring (e.g., the first occurrence of ≥35 dBZ echoes), observations at high spatial and temporal resolutions from weather radars and geostationary meteorological satellites can reveal precursor information such as the boundary-layer convergence lines and the rapid growth of newborn cumulus clouds. These radar- and satellite-observed precursor information are helpful for evaluating the pre-CI conditions and thus nowcasting the accurate CI timing and location. This paper reviewed the current status of radar- and satellite-based CI research and nowcasting techniques. The milestone works and the following studies in the last four decades were summarized to demonstrate how radar and satellite observations can be related to CI occurrence. The objectives and approaches of the CI research advance as the improvement in the capability of radars and were explained satellites. The research progress aids in the development of various CI nowcasting techniques. This paper introduced three well-established techniques that have been put into operational application, namely, ANC system, SATCAST algorithm, and UWCI algorithm. Some scientific issues with respect to radar- and satellite-based CI research and nowcasting were also presented.