The colloquium will present the results recently obtained in fundamental mechanics of multiphase flow through porous media. Physical effects produced by the interaction of the natural flow nonlinearity with medium heterogeneity and coupled compositional, thermal, chemical, capillary and microbiological phenomena, will constitute the program kernel, along with the conceptual mathematical models of such processes. This will cover the theory of liquid displacement by gas with dissolution of chemical components, the thermal drying or ice thawing in saturated media as a kind of Stephan problem, the flow micro-mechanics, the theory of non-equilibrium flow caused by the formation of large-scale phase aggregates, the flow coupled with population dynamics caused by active bacteria or dispersed phase ganglia, the Saffman-Taylor instability amplified or reduced by medium heterogeneity and superposed with hydrodynamic dispersion.