Systems, apparatuses, and methods related to a memory device and an associated host device are described. The memory device and the host device can include control logic that allow the memory device and host device to share refresh-timing information, which may allow either the memory device or the host, or both, to manage operations during time that is dedicated to, but unused for, refresh or self-refresh operations. Refresh-timing information shared from the host device may indicate elapsed time since the host device issued a refresh command to the memory device and/or how much time remains before the host device is scheduled to issue another refresh command. Refresh-timing information shared from the memory device may indicate elapsed time since the memory device performed a self-refresh operation and/or how much time remains before the memory device is scheduled to initiate or undergo another self-refresh operation.