  I survey the use and impact of adaptive mesh refinement (AMR) simulations in
numerical astrophysics and cosmology. Two basic techniques are in use to extend
the dynamic range of Eulerian grid simulations in multi-dimensions: cell
refinement, and patch refinement, otherwise known as block-structured adaptive
mesh refinement (SAMR). In this survey, no attempt is made to assess the
relative merits of these two approaches. Rather, the discussion focuses on how
AMR is being used and how AMR is making a scientific impact in a diverse set of
fields from space physics to the cosmology of the early universe. The increased
adoption of AMR techniques in the past decade is driven in part by the public
availability of AMR codes and frameworks. I provide a partial list of resources
for those interested in learning more about AMR simulations.
