Understanding the physics of Solar Energetic Particle (SEP) events is of importance to the general question of particle energization throughout the cosmos as well as playing a role in the technologically critical impact of space weather on society. The largest, and often most damaging, events are the so-called gradual SEP events, generally associated with shock waves driven by coronal mass ejections (CMEs). We review the current state of knowledge about particle acceleration at evolving interplanetary shocks with application to SEP events that occur in the inner heliosphere. Starting with a brief outline of recent theoretical progress in the field, we focus on current observational evidence that challenges conventional models of SEP events, including complex particle energy spectra, the blurring of the distinction between gradual and impulsive events, and the difference inherent in particle acceleration at quasi-parallel and quasi-perpendicular shocks. We also review the important problem of the seed particle population and its injection into particle acceleration at a shock.