This paper presents a general, fully Bayesian framework for sparse supervised-learning problems based on the horseshoe prior. The horseshoe prior is a member of the family of multivariate scale mixtures of normals, and is therefore closely related to widely used approaches for sparse Bayesian learning, including, among others, Laplacian (LASSO) and Student-t priors (relevance vector machines). The advantages of the horseshoe are its robustness at handling unknown sparsity and large outlying signals. These properties are justified theoretically via a representation theorem and accompanied by comprehensive empirical experiments that compare its performance to benchmark alternatives.