Collaborative Virtual Environments (CVEs) are an exciting advance in the field of Virtual Reality (VR) research. By joining VR systems---and users---at widely scattered geographic locations, VR changes from an isolated experience to one of communication, interaction, and collaboration. Much research effort is being placed into the development of tools and techniques to power these collaborative experiences.;This dissertation describes the Datura toolkit for CVE development and, more importantly, the new concepts and methods that make Datura unique. We focus on the idea of Location of Computation (LoC)---methods for determining where, among all the sites participating in a CVE, particular calculations or particular decisions should be made. Datura connects sites into a peer to peer network, allowing each one to participate fully in bringing the virtual world to life.;Datura works at the level of elements---individual components that imbue shared objects with data, behaviors, and capabilities. These elements are shared among all sites, and control over them can be granted or migrated individually. This dissertation discusses the mechanisms for transferring control and computation, and provides a system for deciding where control should reside for each element in a CVE. An extensive set of tests and evaluations are also described, verifying the capabilities of the Datura system and demonstrating the performance and error-handling gains that are made by this fine-grained control over the location of computation.