The origin of ultrahigh energy cosmic rays (UHECRs) - protons and ions striking our atmosphere with energies extending beyond 1e20 eV - has been an open question for decades. In this talk I will review what we know about UHECRs from an observational and theoretical perspective, focusing particularly on diffusive shock acceleration (DSA). Focusing particularly on radio galaxies, I will discuss some general plasma physics relating to DSA, which can be used to derive some physical requirements for possible sources. Aided by hydrodynamic simulations, I will show that shocks can be formed in backflows in the lobes of radio galaxies and that these shocks can accelerate particles to ultrahigh energy. I will discuss a model in which radio galaxies such as Centaurus A and Fornax A act as slowly-leaking UHECR reservoirs, and consider the escape of UHECRs from the lobes. These radio galaxies are also compelling sources for explaining the observed UHECR arrival directions.