The continuously increasing renewable energy sources (RES) and demand response (DR) are becoming crucial sources of system flexibility. Consequently, decision-dependent uncertainties (DDUs), interchangeably referred to as endogenous uncertainties, impose new characteristics on power system dispatch. The DDUs faced by system operators originate from uncertain dispatchable resources such as RES units or DR, while reserve providers encounter DDUs from the uncertain reserve deployment. Thus, a systematic framework was established in this study to address robust dispatch problems with DDUs. The main contributions are drawn as follows. ① The robust characterization of DDUs was unfolded with a dependency decomposition structure. ② A generic DDU coping mechanism was manifested as the bilateral matching between uncertainty and flexibility. ③ The influence of DDU incorporation on the convexity/non-convexity of robust dispatch problems was analyzed. ④ Generic solution algorithms adaptive for DDUs were proposed. Under this framework, the inherent distinctions and correlations between DDUs and decision-independent uncertainties (DIUs) were revealed, laying a fundamental theoretical foundation for the economic and reliable operation of RES-dominated power systems. Illustrative applications in the source and demand sides are provided to show the significance of considering DDUs and demonstrate the proposed theoretical results.