Einstein’s theory of general relativity (GR) is an elegant and experimentally well tested theory of gravity. From this point of view it may not be too surprising that modifying GR will lead to trouble. This talk will review some of the difficulties in different theoretical approaches of giving the graviton a small mass and some the recent successes in this direction. In particular, the focus will be on three dimensional higher-derivative models of massive gravity. When considered at a critical point in their parameter space, these models become the duals of logarithmic conformal field theories.