This paper studies the consensus problem for multi-agent systems with quantised information communication via event-triggered control. First, the asynchronous event-triggered control for multi-agent systems is considered based on distributed uniform-quantised protocols. It is shown that practical consensus among agents is guaranteed and occurrence of Zeno behaviour is prevented under the designed event-triggering mechanisms. Second, under the proposed protocols using logarithmic quantised information, both synchronous and asynchronous event-triggered control algorithms are given to solve the practical consensus problem. Meanwhile, Zeno behaviour of the closed-loop systems can be excluded under the proposed event-triggered algorithms. Finally, numerical simulations are given to illustrate the effectiveness of the derived results.