Molecular replacement is a method for solving the crystallographic phase problem using an atomic model for the target structure. State-of-the-art methods have moved the field significantly from when it was first envisaged as a method for solving cases of high homology and completeness between a model and target structure. Improvements brought about by application of maximum likelihood statistics mean that various errors in the model and pathologies in the data can be accounted for, so that cases hitherto thought to be intractable are standardly solvable. As a result, molecular replacement phasing now accounts for the lion's share of structures deposited in the Protein Data Bank. However, there will always be cases at the fringes of solvability. I discuss here the approaches that will help tackle challenging molecular replacement cases.