The energetic relics of supernova explosions are reservoirs of enormous amounts of energy. The spin-down of rapidly-rotating, highly-magnetic pulsars forms winds of relativistic particles that, with additional acceleration in the termination shock regions, fill nebulae with particles whose energies exceed many tens of TeV. Rapid shocks in supernova remnants act as particle accelerators to potentially even higher energies. Both supernova remnants and pulsar wind nebulae are thus prime candidates for the production of gamma-rays. The spectra and spatial distribution of these gamma-rays probe crucial physics pertaining to the sites and mechanisms for particle acceleration, and to the long-term evolution of these systems, and Fermi observations are poised to address long-standing questions in these areas. Here I present a summary of the high-energy emission from supernova remnants and pulsar wind nebulae, and highlight new and anticipated results from the Fermi era.