The authors develop the theory of regular variation for measures on general metric spaces, extending the notion of regular variation for Borel measures on the Euclidean space \(\mathbb{R}^d\). To this end, they present an appropriate notion of convergence of measures, including a Portmanteau theorem, a mapping theorem and characterizations of relative compactness. They prove the equivalence of several definitions of regular variation for measures on a complete separable metric space. To illustrate the theory, they derive results concerning regular variation for measures on the spaces \({\mathbb{R}}^{d}\), on the space of continuous functions \({\mathbf C}([0,1];\mathbb{R}^d)\) with the uniform topology, and on the space \(\mathbf D([0,1];\mathbb{R}^d)\) of càdlàg functions with the Skorohod \(J_1\) topology.