This paper investigates the leader-following consensus issue with event/self-triggered schemes under an unreliable network environment. First, we characterize network communication and control protocol update in the presence of denial-of-service (DoS) attacks. In this situation, an event-triggered communication scheme is first proposed to effectively schedule information transmission over the network possibly subject to malicious attacks. In this communication framework, synchronous and asynchronous updated strategies of control protocols are constructed to achieve leader-following consensus in the presence of DoS attacks. Moreover, to further reduce the cost induced by event detection, a self-triggered communication scheme is proposed in which the next triggering instant can be determined by computing with the most updated information. Finally, a numerical example is provided to verify the effectiveness of the proposed communication schemes and updated strategies in the unreliable network environment.