Estimating the evolutionary history of organisms, phylogenetic inference, is a critical step in many analyses involving biological sequence data such as DNA. The likelihood calculations at the heart of the most effective methods for statistical phylogenetic analyses are extremely computationally intensive, and hence these analyses become a bottleneck in many studies. Recent progress in computer hardware, specifically the increase in pervasiveness of highly parallel, many-core processors has created opportunities for new approaches to computationally intensive methods, such as those in phylogenetic inference. We have developed an open source library, BEAGLE, which uses parallel computing methods to greatly accelerate statistical phylogenetic inference, for both maximum likelihood and Bayesian approaches. BEAGLE defines a uniform application programming interface and includes a collection of efficient implementations that use NVIDIA CUDA, OpenCL, and C++ threading frameworks for evaluating likelihoods under a wide variety of evolutionary models, on GPUs as well as on multi-core CPUs. BEAGLE employs a number of different parallelization techniques for phylogenetic inference, at different granularity levels and for distinct processor architectures. On CUDA and OpenCL devices, the library enables concurrent computation of site likelihoods, data subsets, and independent subtrees. The general design features of the library also provide a model for software development using parallel computing frameworks that is applicable to other domains. BEAGLE has been integrated with some of the leading programs in the field, such as MrBayes and BEAST, and is used in a diverse range of evolutionary studies, including those of disease causing viruses. The library can provide significant performance gains, with the exact increase in performance depending on the specific properties of the data set, evolutionary model, and hardware. In general, nucleotide analyses are accelerated on the order of 10-fold and codon analyses on the order of 100-fold.