  We present a summary of the progress made in the last few years on
topological quantum field theory in four dimensions. In particular, we describe
the role played by duality in the developments which led to the Seiberg-Witten
invariants and their relation to the Donaldson invariants. In addition, we
analyze the fruitful framework that this connection has originated. This
analysis involves the study of topological quantum field theories which contain
twisted N=2 supersymmetric matter fields as well as theories obtained after
twisting N=4 supersymmetry. In the latter case, we present some recent results
including the generalization of the partition function of the Vafa-Witten
theory for gauge group SU(N) with prime N.
