An apparatus, comprising: a graphics processing unit GPU comprising a plurality of storage locations and a plurality of execution units; wherein the plurality of execution units are configured to execute GPU commands for each of a plurality of virtual GPUs implemented by the GPU; wherein a priority level for a given GPU command is based on a priority level of a corresponding one of the plurality of virtual GPUs; wherein, for each one of the plurality of virtual GPUs implemented by the GPU, a corresponding one of the plurality of storage locations includes: first and second storage areas configured to store intermediate results, wherein the first and second storage areas are respectively configured to store intermediate vertex-processing results corresponding to that virtual GPU and intermediate pixel-processing results corresponding to that virtual GPU; and wherein the intermediate vertex-processing results are usable to resume execution of one or more incomplete vertex-processing operations for that virtual GPU, and wherein the intermediate vertex-processing results are usable to resume execution of one or more incomplete pixel-processing operations for that virtual GPU characterized in that the GPU is configured to map virtual address space for each of the plurality of virtual GPUs implemented by the GPU to physical memory; and the GPU is configured to allocate a greater portion of physical memory to a higher priority one of the plurality of virtual GPUs and to allocate a lesser portion of physical memory to a lower priority one of the virtual GPUs. a graphics processing unit GPU comprising a plurality of storage locations and a plurality of execution units; wherein the plurality of execution units are configured to execute GPU commands for each of a plurality of virtual GPUs implemented by the GPU; wherein a priority level for a given GPU command is based on a priority level of a corresponding one of the plurality of virtual GPUs; wherein, for each one of the plurality of virtual GPUs implemented by the GPU, a corresponding one of the plurality of storage locations includes: first and second storage areas configured to store intermediate results, wherein the first and second storage areas are respectively configured to store intermediate vertex-processing results corresponding to that virtual GPU and intermediate pixel-processing results corresponding to that virtual GPU; and wherein the intermediate vertex-processing results are usable to resume execution of one or more incomplete vertex-processing operations for that virtual GPU, and wherein the intermediate vertex-processing results are usable to resume execution of one or more incomplete pixel-processing operations for that virtual GPU characterized in that the GPU is configured to map virtual address space for each of the plurality of virtual GPUs implemented by the GPU to physical memory; and the GPU is configured to allocate a greater portion of physical memory to a higher priority one of the plurality of virtual GPUs and to allocate a lesser portion of physical memory to a lower priority one of the virtual GPUs. first and second storage areas configured to store intermediate results, wherein the first and second storage areas are respectively configured to store intermediate vertex-processing results corresponding to that virtual GPU and intermediate pixel-processing results corresponding to that virtual GPU; and wherein the intermediate vertex-processing results are usable to resume execution of one or more incomplete vertex-processing operations for that virtual GPU, and wherein the intermediate vertex-processing results are usable to resume execution of one or more incomplete pixel-processing operations for that virtual GPU characterized in that the GPU is configured to map virtual address space for each of the plurality of virtual GPUs implemented by the GPU to physical memory; and the GPU is configured to allocate a greater portion of physical memory to a higher priority one of the plurality of virtual GPUs and to allocate a lesser portion of physical memory to a lower priority one of the virtual GPUs.