TeV gamma rays, the highest energy photons ever observed, provide a unique window into the non-thermal universe. They are used to study particle acceleration in the Milky Way and beyond, probe the properties of intergalactic space, and search for physics beyond the Standard Model. In this talk I will review searches for particle acceleration with the High Altitude Water Cherenkov (HAWC) obervatory, an air shower array located in central Mexico. The HAWC Collaboration is carrying out a wide-angle survey of TeV gamma rays and cosmic rays from the Northern hemisphere. I will highlight measurements of gamma rays from a nearby accelerator which provide evidence for a population of particles with energies up to 1 PeV. I will then discuss implications of these measurements for current models of particle acceleration.