A system, method and computer program product for virtualizing a processor and its memory, including a host operating system (OS); and virtualization software that maintains a virtualization environment for running a Virtual Machine (VM) without system level privileges and having a guest operating system running within the Virtual Machine. A plurality of processes are running within the host OS, each process having its own virtual memory, wherein the virtualization software is one of the processes. A host OS swap file is stored in persistent storage and maintained by the host operating system. The host OS swap file represents virtualized physical memory of the VM. A plurality of memory pages are aggregated into blocks, the blocks being stored in the host OS swap file and addressable in block form. The virtualization software manages the blocks so that blocks can be mapped to the virtualization software process virtual memory and released when the blocks are no longer necessary. The host OS swaps the blocks between the host OS swap file and physical memory when a block that is not in physical memory is accessed by the VM. The host OS swap file size is not subject to limitation on virtual process memory size. A user of the VM can access a larger virtual process memory than the host OS permits.