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This brief studies distributed containment control for double-integrator dynamics in the presence of both stationary and dynamic leaders. In the case of stationary leaders, we propose a distributed containment control algorithm and study conditions on the network topology and the control gains to guarantee asymptotic containment control in any dimensional space. In the case of dynamic leaders, we study two cases: leaders with an identical velocity and leaders with nonidentical velocities. For the first case, we propose two distributed containment control algorithms to solve, respectively, asymptotic containment control under a switching directed network topology and finite-time containment control under a fixed directed network topology. In particular, asymptotic containment control can be achieved for any dimensional space if the network topology is fixed and for only the 1-D space if the network topology is switching. For the second case, we propose a distributed containment control algorithm under a fixed network topology where the communication patterns among the followers are undirected and derive conditions on the network topology and the control gains to guarantee asymptotic containment control for any dimensional space. Both simulation results and experimental results on a multi-robot platform are provided to validate some theoretical results.