This chapter discusses the possibility of instilling a virtual world with mechanisms for evolution and natural selection in order to generate rich ecosystems of complex organisms in a process akin to biological evolution. Some previous work in the area is described, and successes and failures are discussed. The components of a more comprehensive framework for designing such worlds are mapped out, including the design of the individual organisms, the properties and dynamics of the environmental medium in which they are evolving, and the representational relationship between organism and environment. Some of the key issues discussed include how to allow organisms to evolve new structures and functions with few restrictions, and how to create an interconnectedness between organisms in order to generate drives for continuing evolutionary activity. 1 According to the neo-Darwinist theory of evolution, the richness and complexity of biological life can be explained in terms of three fundamental processes: reproduction, heritable variation, and competition for limited resources leading to natural selection. The beautiful simplicity of this picture raises the intriguing question: might it be possible to instill these processes in a virtual world, and, in so doing, unleash an ongoing evolutionary process that populates that world with a rich ecosystem of complex virtual organisms?Attempts to do precisely this have a history as long as that of the modern digital computer itself. This chapter starts with a brief review of past work and the current state of the art; although much of this work is remarkable, the quest for open-ended evolution remains elusive; after an initial burst of activity, these systems tend to quickly reach a quasi-stable state beyond which no further qualitative changes are observed.These results raise a nagging question: just how far can evolution progress in such worlds beyond what is easily discoverable by virtue of the specific way in which the world has been designed? The nature of these systems is examined in order to address this question.