  We study a unitary matrix model with Gross-Witten-Wadia weight function and
determinant insertions. After some exact evaluations, we characterize the
intricate phase diagram. There are five possible phases: an ungapped phase, two
different one-cut gapped phases and two other two-cut gapped phases. The
transition from the ungapped phase to any gapped phase is third order, but the
transition between any one-cut and any two-cut phase is second order. The
physics of tunneling from a metastable vacuum to a stable one and of different
releases of instantons is discussed. Wilson loops, $\beta$-functions and
aspects of chiral symmetry breaking are investigated as well. Furthermore, we
study in detail the meromorphic deformation of a general class of unitary
matrix models, in which the integration contour is not anchored to the unit
circle. The ensuing phase diagram is characterized by symplectic singularities
and captured by a Hasse diagram.
