Capacitive deionization is a water desalination technology in which ions are stored in electrodes in an electrochemical cell construction, connected to an external circuit, to remove ions present in water from various sources. Conventionally, carbon has been the choice of material for the electrodes due to its low cost, low contact resistance and high specific surface area, electronic conductivity, and ion mobility within pores. The ions in the water are stored at the pore walls of these electrodes in an electrical double layer. However, alternative electrode materials, with a different mechanism for ion and charge storage, referred to as ion intercalation, have been fabricated and studied as well. The salt adsorption performance exhibited by these materials is in most cases higher than that of carbon electrodes. This work traces the evolution of the study of redox activity in these intercalation materials and provides a chronological description of major developments in the field of Capacitive Deionization (CDI) with intercalation electrodes. In addition, some insights into the cell architecture and operation parameters are provided and we present our outlook of future developments in the field of intercalation materials for CDI.