In this study, the containment control problems in second-order multi-agent systems for both static leaders and dynamic leaders under directed topologies are studied. The authors propose the impulsive containment control algorithms without using velocity measurements. Some necessary and sufficient conditions depending on the eigenvalues of the Laplacian matrix associated with the communication graph, the impulsive period and the gain parameters, are obtained to guarantee the containment control. Then, the containment control of multi-agent systems with input delay using impulsive algorithms is investigated. Also, some necessary and sufficient conditions are given. Finally, some simulations are conducted to verify the effectiveness of the proposed algorithms.