We present BUSTED, a new approach to identifying gene-wide evidence of episodic positive selection, where the non-synonymous substitution rate is transiently greater than the synonymous rate. BUSTED can be used either on an entire phylogeny (without requiring an a priori hypothesis regarding which branches are under positive selection) or on a pre-specified subset of foreground lineages (if a suitable a priori hypothesis is available). Selection is modeled as varying stochastically over branches and sites, and we propose a computationally inexpensive evidence metric for identifying sites subject to episodic positive selection on any foreground branches. We compare BUSTED with existing models on simulated and empirical data. An implementation is available on www.datamonkey.org/busted, with a widget allowing the interactive specification of foreground branches.