Self-assembly is expected to become a dominant fabrication technique for the nanodevices and systems of the future. Traditional, or passive, self-assembly techniques have great difficulty in producing the asymmetric structures needed by the applications. This work discusses self-assembly methods that use active assembly agents (robots). It shows that swarms of such robots that communicate only by very simple messages can be programmed to form either wholly or partially specified structures, with the construction process possibly involving sacrificial components or scaffolds. The assembly agents have small memory and communication requirements, and interact only when they are in contact. They are good models for future nanorobots, which are likely to communicate chemically.