Chemical and structural complexity has proved to be an critical factor in producing a variety of fascinating properties of solids, including ferroelectricity, large piezoelectric and dielectric responses, and multiferroicity in metals and insulators, as well as quasicrystallinity and high-temperature superconductivity. The research in my group currently centers on the theoretical investigation of ferroelectrics and related materials, and of magnetic and nonmagnetic martensites. First-principles density-functional methods are used both directly and in the construction of first-principles effective Hamiltonians for theoretical prediction and analysis of properties of materials, both real and as-yet hypothetical, in bulk and thin film forms.