This article provides an overview of the use of theory and computation to describe the structural, thermodynamic, mechanical, and optical properties of nanoscale materials. Nanoscience provides important opportunities for theory and computation to lead in the discovery process because the experimental tools often provide an incomplete picture of the structure and/or function of nanomaterials, and theory can often fill in missing features crucial to understanding what is being measured. However, there are important challenges to using theory as well, as the systems of interest are usually too large, and the time scales too long, for a purely atomistic level theory to be useful. At the same time, continuum theories that are appropriate for describing larger-scale (micrometer) phenomena are often not accurate for describing the nanoscale. Despite these challenges, there has been important progress in a number of areas, and there are exciting opportunities that we can look forward to as the capabilities of computational facilities continue to expand. Some specific applications that are discussed in this paper include: self-assembly of supramolecular structures, the thermal properties of nanoscale molecular systems (DNA melting and nanoscale water meniscus formation), the mechanical properties of carbon nanotubes and diamond crystals, and the optical properties of silver and gold nanoparticles.