Time delay is another source of uncertainty appearing in any communication network. While in most scenarios, time delay decreases the system’s performance, small time delays may also provide a stabilization effect. This chapter is devoted to studying the stability of matrix-weighted consensus over an undirected matrix-weighted graph G under the presence of constant time delays. First, given the knowledge of the matrix-weighted Laplacian, several conditions are derived to ensure a consensus is achieved asymptotically. If there is only a uniform time delay in the network, a necessary and sufficient condition is derived. An upper bound for the time delay is provided so that unless the time delay exceeds the upper bound, a consensus is asymptotically achieved. It is interesting that the upper bound involves only the largest eigenvalue of the matrix-weighted Laplacian. Second, the matrix-weighted consensus with heterogeneous constant time delays associated with several subgraphs of the graph G is considered. The Lyapunov–Krasovskii theorem is then invoked to determine a corresponding stability condition, which also suggests an upper bound for the time delays. Third, based on the observation that the eigenvalues of the matrix-weighted Laplacian are directly related with the upper bound of time delay, an adaptive algorithm is proposed to alter the consensus update gain and actively expand the upper bound for the unknown time delays. By this way, the proposed adaptive algorithm provides a simple method to deal with time delay, when only a single or multiple constant time delays are present in the network.