The paper provides characterizations of controllability of the differential inclusion x'(t)\(\in A(x(t))\) where A is a convex process from \(R^ n\) into itself. As expected, controllability is equivalent to observability of the associated adjoint inclusion \(-q'(t)\in A^*(x(t))\) where \(A^*\) denotes the transpose of A. Other characteristic properties are couched in terms of classical notions appropriately extended to the case of convex processes: invariant cones, viability domains, eigenvalues, eigenvectors, and a rank condition. Typical known results concerning controllability or local controllability of linear autonomous systems in \(R^ n\) are derived or generalized by specializing the convex process A.