1. A computer-implemented method comprising: in response to information provided by a client, storing, by one or more configured computing systems of a constraint manager network service, a defined group of one or more constraints that each specify a criterion for computing-related resources used on behalf of the client by other network services, the defined group including at least one constraint that specifies one or more geographical locations in which the computing-related resources are to be located; associating, by the one or more configured computing systems, a reference with the defined group of one or more constraints; receiving, by the one or more configured computing systems, a request from a first network service indicating the associated reference for information about the one or more constraints that correspond to the reference, and providing information about the one or more constraints to the first network service; receiving, by the one or more configured computing systems, information from the first network service about one or more computing-related resources that are provided by the first network service for use on behalf of the client in a manner that satisfies the one or more constraints; receiving, by the one or more configured computing systems and subsequent to the receiving of the information from the first network service, a request from a second network service indicating the associated reference for information about the one or more constraints that correspond to the reference, the second network service being distinct from the first network service; and providing information to the second network service about the one or more constraints and about the one or more computing-related resources provided by the first network service, the provided information enabling the second network service to use one or more other computing-related resources in a manner that satisfies the one or more constraints and that is based at least in part on the one or more computing-related resources.