This review focusses on polyanhydrides, a fascinating class of degradable polymers that have been used in and investigated for many bio-related applications because of their degradability and capacity to undergo surface erosion. This latter phenomenon is driven by hydrolysis of the anhydride moieties at the surface and high hydrophobicity of the polymer such that degradation and mass loss (erosion) occur before water can penetrate deep within the bulk of the polymer. As such, when surface-eroding polymers are used as therapeutic delivery vehicles, the rate of delivery is often controlled by the rate of polymer erosion, providing predictable and controlled release rates that are often zero-order. These desirable attributes are heavily influenced by polymer composition and morphology, and therefore also monomer structure and polymerization method. This review examines approaches for polyanhydride synthesis, discusses their general thermomechanical properties, surveys their hydrolysis and degradation processes along with their biocompatibility, and looks at recent developments and uses of polyanhydrides in drug delivery, stimuli-responsive materials, and novel nanotechnologies.