This paper presents an event-triggered control and communication framework for the cooperative leader-tracking problem with communication constraints. Continuous communication among agents is not assumed in this work and decentralised event-based strategies are proposed for agents with heterogeneous linear dynamics. Also, the leader dynamics are unknown and only intermittent measurements of its states are obtained by a subset of the followers. The event-based method not only represents a way to restrict communication among agents, but it also provides a decentralised scheme for scheduling information broadcasts. Notably, each agent is able to determine its own broadcasting instants independently of any other agent in the network. In an extension, the case where transmission of information is affected by time-varying communication delays is addressed. Finally, positive lower-bounds on the inter-event time intervals are obtained in order to show that Zeno behaviour does not exist and, therefore, continuous exchange of information is never needed in this framework.