This article develops a framework for treating multiagent consensus problems using quantised control. Specifically, we present asymmetrically and symmetrically quantised consensus protocols for multiagent dynamical systems. The proposed consensus protocols involve the exchange of quantised information between agents. Due to quantisation, the requirement for consensus is weakened to quantised near-consensus. Under certain assumptions on the network topology, the proposed protocols guarantee that the closed-loop dynamical network is Lyapunov stable and convergent to an appropriately defined set in finite time. We present a complete stability and convergence analysis, using dynamical systems theory and Lyapunov-based approaches. The quasi-robustness of the symmetrically quantised consensus protocols to slowly-varying communication errors is analysed. To the best of our knowledge this is the first time such an analysis has been presented in the literature. Several simulation examples illustrate the main results of this article.