My talk will consist of three subtopics. The brain remembers episodes not in isolation but with their contextual relationships, such as spatial or temporal proximity. This is an essential feature of the brain’s memory, but the underlying mechanism is yet to be explored. Cell assemblies, or engrams, may provide neural representations for such relationships. First, I will show a class of associative memory models that encode and retrieve multiple memory contents linked by an arbitrary graph structure through experience and demonstrate the crucial role of the balance between two inhibitory subnetwork types in the flexible retrieval of relational memories. Secondly, I propose a theoretical framework to generate a cognitive map, i.e., neural representations of relationships between memory items. This framework aims at the predictive function of the hippocampus and is based on successor representations proposed for reinforcement learning. Intriguingly, the model provides a unified account for grid cells in spatial navigation and concept cells in natural language processing. Finally, I will discuss another crucial role of the hippocampal memory system, memory replay, in a spiking neural network model. Unlike the conventional associative memory models that maintain attractor memory states, this model attempts to maximize the capacity of replayed activity patterns. Our model suggests the crucial role of inhibitory plasticity in optimizing spontaneous memory replay.