This chapter explores discrete-time matrix-weighted consensus algorithms that enable the state vectors of all agents to asymptotically agree without requiring continuous updation of the relative states. First, a discrete-time matrix-weighted consensus algorithm obtained by discretizing the continuous-time matrix-weighted consensus algorithm is considered under various assumptions about the topologies of a matrix-weighted network. Second, a gossip-based randomized matrix-weighted consensus algorithm is presented. By letting the updating sequences and instances be governed by a stochastic process, the algorithm greatly reduces communication costs and mitigates the need for strict clock synchronization in synchronized updates. The chapter also presents an application of the randomized algorithm in bearing-based network localization.