We investigate domain-wall/quantum field-theory correspondences in various dimensions. Our general analysis covers not only the well studied cases in 10 and 11 dimensions, but also enables us to discuss new cases like a type I/heterotic 6-brane in 10 dimensions and domain-wall dualities in lower than 10 dimensions. The examples we discuss include `d-branes' in six dimensions preserving eight supersymmetries and extreme black holes in various dimensions. In the latter case we construct the quantum mechanics Hamiltonian and discuss several limits.