The theory of the acceleration of auroral particles is reviewed, focusing on developments in the last 15 years. We discuss elementary plasma physics processes leading to acceleration of electrons to energies compatible with emission observed for quiet, discrete auroral arcs, defined as arcs that have time scales of minutes or more and spatial scales ranging from less than 1 km to tens of kilometers. For context, earlier observations are first described briefly. The theoretical fundamentals of auroral particle acceleration are based on the kinetic theory of plasmas, in particular the development of parallel electric fields. These parallel electric fields can either be distributed along the magnetic field lines, often associated with the mirror geometry of the geomagnetic field, or concentrated into narrow regions of charge separation known as double layers. Observations have indicated that the acceleration process depends on whether the field-aligned currents are directed away from the Earth, toward the Earth, or in mixed regions of currents often associated with the propagation of Alfvén waves. Recent observations from the NASA Fast Auroral SnapshoT (FAST) satellite, the ESA satellite constellation Cluster, and the Japanese Reimei satellite have provided new insights into the auroral acceleration process and have led to further refinements to the theory of auroral particle acceleration.