  An S-fold has played an important role in constructing supersymmetric field
theories with interesting features. It can be viewed as a type of AdS_4
solutions of Type IIB string theory where the fields in overlapping patches are
glued by elements of SL(2,Z). This paper examines three dimensional quiver
theories that arise from brane configurations with an inclusion of the S-fold.
An important feature of such a quiver is that it contains a link, which is the
T(U(N)) theory, between two U(N) groups, along with bifundamental and
fundamental hypermultiplets. We systematically study the moduli spaces of those
quiver theories, including the cases in which the non-zero Chern-Simons levels
are turned on. A number of such moduli spaces turns out to have a very rich
structure and tells us about the brane dynamics in the presence of an S-fold.
