Focused electron-beam-induced (FEB-induced) deposition and etching are versatile, direct-write nanofabrication schemes that allow for selective deposition or removal of a variety of materials. Fundamentally, these processes are governed by an electron-induced reaction with a precursor vapor, which may either result in decomposition to a solid deposit or formation of a volatile etch by-product. The ability to induce such localized reactions by placement of a nanometer-sized focused electron probe has recently drawn considerable attention. In response, we have reviewed much of the relevant literature pertaining to both focused electron-beam-induced etching and deposition. Because these nanoscale processing techniques are still in their relative infancy, a significant amount of scientific research is being conducted to understand, and hence improve, the processes. This article summarizes the associated physics of electron-solid-vapor interactions, discusses related physical processes, and provides an introduction to electron-beam-induced etching (EBIE) and electron-beam-induced deposition (EBID). Additionally, specific applications of FEB-induced processes are discussed and several FEB computer model and simulation results are reviewed.