Processing within a computing environment that supports pageable guests is facilitated. Processing is facilitated in many ways, including, but not limited to, associating guest and host state information with guest blocks of storage; maintaining the state information in control blocks in host memory; enabling the changing of states; and using the state information in management decisions. In one particular example, the guest state includes an indication of usefulness and importance of memory contents to the guest, and the host state reflects the ease of access to memory contents. The host and guest state information is used in managing memory of the host and/or guests.