"Systems of hydrodynamic type are first-order quasi-linear PDEs (partial differential equations). Their solutions are generically singular. As certain limits of more general nonlinear PDEs, modelling e.g. the evolution of physical systems, they describe critical phenomena, like shock waves. An embedding in (or deformation to) a more general nonlinear PDE typically ""regularises"" such a critical phenomenon and introduces specific features. The question how such a catastrophe becomes noticeable near a corresponding critical event is of uttermost importance, in particular for its prediction in nature. Moreover, explorations in 1+1 space-time dimensions led to a conjecture (Boris Dubrovin, 2006) of a universal behavior of solutions near such critical events, governed by an exceptional class of differential equations, the Painleve equations. In this project, hydrodynamic-type systems are addressed as limiting cases of integrable PDEs, for which a large class of exact solutions can be constructed and powerful analytical methods are available. It concentrates on equations in 2+1 space-time dimensions, which in this respect is fairly unexplored terrain. Three complementary methods are employed for a corresponding exploration: hydrodynamic reductions, bidifferential calculus, and numerical analysis in the critical regime."