In this talk, we review various subspace techniques that are used in constructing numerical methods for optimization. The subspace techniques are getting more and more important as the optimization problems we have to solve are getting larger and larger in scale. The essential part of a subspace method is how to choose the subspace in which the trial step or the trust region should belong. Model subspace algorithms for unconstrained optimization, constrained optimization, nonlinear equations and matrix optimization problems are given respectively, and different proposals are made on how to choose the subspaces.