  In this informal review for non-specalists we discuss the construction of
maximally supersymmetric gauge theories that arise on the worldvolumes branes
in String Theory and M-Theory. Particular focus is made on the relatively
recent construction of M2-brane worldvolume theories. In a formal sense, the
existence of these quantum field theories can be viewed as predictions of
M-Theory. Their construction is therefore a reinforcement of the ideas
underlying String Theory and M-Theory. We also briefly discuss the
six-dimensional conformal field theory that is expected to arise on M5-branes.
The construction of this theory is not only an important open problem for
M-Theory but also a significant challenge to our current understanding of
quantum field theory more generally.
