Adaptive mesh refinement (AMR) as a numerical method has roots that go well beyond its first application in the field of numerical relativity. Mesh refinement first appears in the numerical relativity literature in the 1980s, through the work of Choptuik in his studies of critical collapse of scalar fields. The original work was in one dimension, but it was subsequently extended to two dimensions. In two dimensions, AMR has also been applied to the study of inhomogeneous cosmologies, and to the study of Schwarzschild black holes. The technique has now become a standard tool in numerical relativity and has been used to study the merger of black holes and other compact objects in addition to the propagation of gravitational radiation generated by such astronomical events.