Observations by NASA's Magnetospheric Multiscale mission have demonstrated that magnetic reconnection occurs at Earth's bow shock, where the solar wind transitions from supersonic to subsonic flow. This is typically associated with thin current sheets arising from plasma instabilities and turbulence in the shock transition region. Here, I will review the observational signatures of reconnection at Earth's bow shock, including surveys of both the shock transition and the magnetosheath downstream. These studies suggest that the number of current sheets in these regions may not be strongly dependent on the shock Mach number or the angle between the upstream magnetic field and shock normal. This result is somewhat surprising given that quasi-parallel and high Mach number shocks tend to have a more disordered and non-stationary structure. We explore this phenomenon further with a series of 2D hybrid (fluid electron, kinetic ion) particle-in-cell simulations across a range of shock parameters. By quantifying reconnection using the area occupied by plasma on closed magnetic field lines, we find a similar result to observational surveys: within the subset of quasi-parallel shocks, the decay rate of the closed field area (and hence thin current sheets) is not strongly dependent on upstream shock parameters. Finally, I will discuss shock reconnection in more complex scenarios, including 3D simulations, and during the impact of solar wind transients (magnetic discontinuities).