Quantum network mainly consists of a memory used for storing and manipulating quantum information and an information carrier through which different memories can connect with others. Usually quantum information is encoded in a two-dimensional space of a photon, a robust information carrier. In this case, each photon can carry a bit of information. If the photon can live in a high-dimensional space, then the information carried by each photon could be increased significantly, the channel capacity of the network and the transmission efficiency would then be greatly enlarged. Moreover, storing high-dimensional states in quantum memory leads to significant improvements in storage capacity. After briefly introducing the progresses achieved at home and abroad, a significant breakthrough was reviewed towards the realization of high-dimensional quantum memories based on a cold atomic ensemble in detail, and some basic problems remaining were proposed which need to be solved to build the future quantum internet.