It is well-known that the singular homology of a Riemannian manifold can be computed from the Morse complex whose chains are generated by the critical points of a Morse function and differential counts the flow lines connecting the critical points. I'll talk about slightly different versions of Morse complexes that can recover homology rel. boundary and equivariant homology. Finally I'll define the Conley index theory which is a generalization of the Morse homology but doesn't require some of its technical transversality conditions.