We study exact metrics on non-compact manifolds with exceptional holonomySpin(7),G2.We derive the metrics by using the formulation with vector fields. We point out that the coordinates on coset spaces are useful to handle the metrics. The coset construction also ensures that the metrics are the solutions of the self-duality condition for the spin connection. Then we conjecture the classification of spacesR×G/HwithSpin(7) holonomy. Finally, we comment on the coset construction of metrics withSU(3)holonomy. ©2002 American Institute of Physics.