  Photo-induced phase-transitions (PIPTs) driven by highly cooperative
interactions are of fundamental interest as they offer a way to tune and
control material properties on ultrafast timescales. Due to strong correlations
and interactions, complex quantum materials host several fascinating PIPTs such
as light-induced charge density waves and ferroelectricity and have become a
desirable setting for studying these PIPTs. A central issue in this field is
the proper understanding of the underlying mechanisms driving the PIPTs. As
these PIPTs are highly nonlinear processes and often involve multiple time and
length scales, different theoretical approaches are often needed to understand
the underlying mechanisms. In this review, we present a brief overview of PIPTs
realized in complex materials, followed by a discussion of the available
theoretical methods with selected examples of recent progress in understanding
of the nonequilibrium pathways of PIPTs.
