  This is a survey paper. We explain the known constructions for two
geometrically different classes of examples of compact Riemannian 7-manifolds
with holonomy G2. One method uses resolutions of singularities of appropriately
chosen 7-dimensional orbifolds, with the help of asymptotically locally
Euclidean spaces. Another method uses the gluing of two asymptotically
cylindrical pieces and requires a certain matching condition for their
cross-sections `at infinity'.
