The notion of a factorizable methods for systems of PDEs of mixed type was introduced within the Eulerian framework for the compressible flow equations about twenty years ago in. It stands for a discretization that reflects the mixed type of the system, i.e. does not introduce any non-physical coupling between different co-factors of the system. Such methods were shown to offer some substantial benefits like a possibility to construct an efficient solver and also an essential unification of treatment of compressible and incompressible flow. It was discovered lately that this property is crucial for the Lagrangian methods. We shall review some recent developments of factorizable methods, both Lagrangian an Eulerian, discuss some outstanding issues and outline future plans.