  In this paper, we study the asymptotic behavior of the solutions of nonlocal
bistable reaction-diffusion equations starting from compactly supported initial
conditions. Depending on the relationship between the nonlinearity, the
interaction kernel and the diffusion coefficient, we show that the solutions
can either: propagate, go extinct or remain pinned. We especially focus on the
latter regime where solutions are pinned by thoroughly studying discontinuous
ground state solutions of the problem for a specific interaction kernel serving
as a case study. We also present a detailed numerical analysis of the problem.
