Cosmic Acceleration and Modified Gravity

I briefly discuss some attempts to construct a consistent modification to General Relativity (GR) that might explain the observed late-time acceleration of the universe and provide an alternative to dark energy. I mention the issues facing extensions to GR, illustrate these with two specific examples, and discuss the resulting observational and theoretical obstacles. This article comprises an invited talk at the NASA workshop {\it From Quantum to Cosmos: Fundamental Physics Research in Space}