This paper investigates the event-triggering containment control of multi-agent networks with fixed and switching topologies, where there exist interactions between the leaders. Two cases are studied, respectively: One is that the leaders are opinionated. Then each leader will converge to its initial goal and the followers converge to the convex hull formed by the leaders. The other is that the leaders are not opinionated. Then the leaders will not insist on their initial goals and converge to some compromising states due to the interactions among them, while the followers still converge to the convex hull formed by the leaders. By means of pull-based event-triggering control, the event-triggering containment control problems of multi-agent systems with fixed and switching topologies are investigated, respectively. Finally, simulations are given to illustrate the theoretical results.