In this paper, we investigate reachable sets for some classes of open- and closed-loop control systems governed by ordinary differential equations. We are particularly interested in convexity properties of both reachable sets and sets of trajectories. If such properties exist they can be used to estimate the reachable set under investigation. This is important in applications as, e.g., the verification of safety properties. Convexity of the set of trajectories is also important for a constructive reformulation of some constrained dynamical optimization problems in the form of a convex minimization problem.