This paper aims to solve two fundamental problems on finite or infinite horizon dynamic games with complete information. Under some mild conditions, we prove the existence of subgame-perfect equilibria and the upper hemicontinuity of equilibrium payoffs in general dynamic games with simultaneous moves (i.e., almost perfect information), which go beyond previous works in the sense that stagewise public randomization and the continuity requirement on the state variables are not needed. For alternating move (i.e., perfect-information) dynamic games with uncertainty, we show the existence of pure-strategy subgame-perfect equilibria as well as the upper hemicontinuity of equilibrium payoffs, extending the earlier results on perfect-information deterministic dynamic games.