There is an increasing interest in using graphene (1, 2) for optoelectronic applications. (3-19) However, because graphene is an inherently weak optical absorber (only ≈2.3% absorption), novel concepts need to be developed to increase the absorption and take full advantage of its unique optical properties. We demonstrate that by monolithically integrating graphene with a Fabry-Pérot microcavity, the optical absorption is 26-fold enhanced, reaching values >60%. We present a graphene-based microcavity photodetector with responsivity of 21 mA/W. Our approach can be applied to a variety of other graphene devices, such as electro-absorption modulators, variable optical attenuators, or light emitters, and provides a new route to graphene photonics with the potential for applications in communications, security, sensing and spectroscopy.