Bionanotechnology is an emerging field in nanotechnology. In general, it uses concepts from chemistry, biochemistry, and molecular biology to identify components and processes for the construction of self-assembling materials and devices. Distant goals of the science of bionanotechnology range from developing programmable nanoscale devices that can sample or alter their environments to developing assemblies capable of Darwinian evolution. At the heart of these approaches is the concept of the production of supramolecular assemblies (SMAs; also known as supramolecular aggregates) by programmed self-assembly in an aqueous medium. Ordered arrays, planar and closed-shell tilings, dynamic machines, and switches have been designed and constructed by using DNA-DNA, protein-protein, and protein-nucleic acid biospecificities. We review the designs and the analytical techniques that have been employed in the production of SMAs that do not occur in nature.