I will review work on the thermodynamics of accelerating black holes. The accelerating black hole is represented by the C-metric - an exact solution in Einstein gravity with conical deficits (of unequal deficit angles) emerging from the poles of the horizon. The black hole is therefore not isolated, but a composite system. I show how to derive the thermodynamics of this composite system, including changes in the angular deficits. I will disentangle the impact of a conical deficit in the spacetime, and the impact of acceleration, as well as proving a new "Reverse Isoperimetric Inequality" for black holes with a deficit.