This article focuses on the problem of resilient leader-following consensus for multiagent systems against denial-of-service (DoS) attacks. Two update strategies based on event/self-triggering are proposed for the control protocols to handle the leader-following consensus in unreliable shared networks. We first propose a dynamic event-triggered communication scheme to mitigate unnecessary information transfer through energy-limited and vulnerable networks. Continuous communication between agents can be avoided. DoS attacks are supposed to be aperiodic and asynchronous at different edges. The concept of valid DoS attack interval is introduced, and the frequency and duration of attacks are analyzed. The leader-following consensus can be achieved when there exist DoS attacks using the dynamic event-based control strategy. Then, to avoid continuous event detection and save computation resources, a self-triggered communication function is developed. The next triggering moment is predetermined with the latest received state information, and the Zeno behavior is eliminated for the feasibility of the event/self-triggering scheme. Finally, a simulation is provided to verify the effectiveness of the proposed update strategies and control protocols.