A data processing apparatus comprises a processor having an internal state dependent upon execution of application program code, the processor being configured to generate display data relating to images to be displayed and to buffer display data relating to a most recent period of execution of a currently executing application. The apparatus includes RAM for storing temporary data relating to a current operational state of program execution. The apparatus also includes a data transfer controller configured to transfer data from the RAM relating to the currently executing application, data relating to a current internal state of the processor and buffered display data to suspend data memory, and to transfer data from the suspend data memory to RAM and to the processor to recreate an execution state of an application at a time the suspend instruction was executed, and to retrieve display data relating to the resumed application.