1. A computer-implemented method for handling metaevents within an on-demand code execution environment, the on-demand code execution environment comprising at least one virtual machine instance executing an initialized operating system and awaiting requests to execute user-specified code within that operating system, the method comprising: as implemented by one or more computing devices configured with specific computer-executable instructions, receiving a request to define a metaevent on the on-demand code execution environment, wherein the metaevent is defined at least partly by satisfaction of a set of metaevent criteria relating to execution of a first set of user-specified code on the on-demand code execution environment, wherein the request specifies the set of metaevent criteria and a job to be executed by the on-demand code execution environment on occurrence of the metaevent by satisfaction of the metaevent criteria, and wherein the job includes execution of a second set of user-specified code, wherein satisfaction of the metaevent criteria requires that execution of the first set of user-specified code has not occurred within a specified time interval on the on-demand code execution environment; obtaining metadata regarding execution of the first set of user-specified code on the on-demand code execution environment, wherein the metadata regarding the operation of the on-demand code execution environment comprises at least one of: an indication of execution of the first set of user-specified code detected at the on-demand code execution environment, information regarding queuing a request to execute the first set of user-specified code at the on-demand code execution environment, information regarding timing of execution of the first set of user-specified code, information regarding throttling of execution the first set of user-specified code, or information regarding results or output of execution first set of user-specified code; analyzing the metadata according to the metaevent criteria to determine that the metadata satisfies the metaevent criteria; and processing the job at least partly by executing the second set of user-specified code within the initialized operating system of the at least one virtual machine instance.