In a general aspect, a hybrid memory system with cache management is disclosed. In some aspects, a memory module includes volatile memory, non-volatile memory, and an internal cache. The internal cache is communicably coupled with the volatile memory and the non-volatile memory. Whether to execute a memory access request is determined by operation of the memory module. In response to the inability of the memory access request to be executed, a data transferring process is performed to copy data between the volatile memory and the non-volatile memory via the internal cache.