The parallel fluidic self-assembly of microdevices is a new technology that promises to speed up the production of complex microsystems made up of many separate parts. The technology brings many advantages. First, it enables a mix of chipmaking technologies for each of the component parts, with each technology selected for its particular technical or financial benefits. Second, it eliminates the need for pickand-place assembly that would unnecessarily slow down any manual assembly technique. Third, it enables massively parallel assembly, almost independent of the number of parts involved, and thereby mimics the elegant parallelism inherent in microchip circuit manufacture.In this chapter we explore this new technology with the ultimate goal of discovering the practical limits for its practical use in manufacturing real microsystems. The driving force of the assembly process is interface surface tension, and our approach is to find the simplest models that correctly describe the attachment, orientation, and bonding of parts to a suitably prepared substrate. We follow both an analytical and a numerical approach in describing the surface tension effects, the latter mainly to gain geometrical generality, and we couple modeling and simulation with suitable laboratory experiments. The ultimate goal of this work is to find practical design rules with which to select bond site geometries and the properties of participating liquids, and to find practical tolerances for all required geometrical and rheological parameters. This chapter extensively documents all results found to date, and carefully cites other work in this area.