Rgtsvm provides a fast and flexible support vector machine (SVM) implementation for the R language. The distinguishing feature of Rgtsvm is that support vector classification and support vector regression tasks are implemented on a graphical processing unit (GPU), allowing the libraries to scale to millions of examples with >100-fold improvement in performance over existing implementations. Nevertheless, Rgtsvm retains feature parity and has an interface that is compatible with the popular e1071 SVM package in R. Altogether, Rgtsvm enables large SVM models to be created by both experienced and novice practitioners.