  We prove a result motivated by Williams's classification of expanding
attractors and the Franks-Newhouse Theorem on codimension-1 Anosov
diffeomorphisms: If a mixing hyperbolic attractor has 1-dimensional unstable
manifolds then it is either is expanding or is homeomorphic to a compact
abelian group (a toral solenoid); in the latter case the dynamics is conjugate
to a group automorphism. As a corollary we obtain a classification of all
2-dimensional basic sets in 3-manifolds. Furthermore we classify all hyperbolic
attractors in 3-manifolds in terms of the classically studied examples,
answering a question of Bonatti.

Dynamical Systems