1. A system for providing low-latency computational capacity from a virtual compute fleet, the system comprising: an electronic data store configured to store at least a program code of a user; and a virtual compute system comprising one or more hardware computing devices executing specific computer-executable instructions, said virtual compute system in communication with the data store, and configured to at least: maintain a plurality of virtual machine instances on one or more physical computing devices, wherein the plurality of virtual machine instances comprise: a warming pool comprising virtual machine instances having one or more software components loaded thereon and waiting to be assigned to a user; and an active pool comprising virtual machine instances currently assigned to one or more users; receive a first code execution request to execute a first program code on the virtual compute system; determine, based on the first code execution request, that the first program code is a newer version of a second program code loaded onto a container created on a particular instance of the virtual machine instances in the active pool; initiate a download of the first program code onto at least one of the internal data store, a code cache of the particular instance, and the container; and process the code execution request with the second program code.