New trends have been traced and the existing ones refined regarding filtration and diffusive motion of gases in coal beds and surrounding rock, spontaneous heating of coal and transport of gas traces by ventilation currents in operating coal mines. Mathematical models of gas-dynamic and thermophysical processes inside underworked territories after mine abandonment have been justified. Mathematical models are given for feasible air feeding of production and development areas, as well as for the development of geotechnical solutions to ensure gas-dynamic safety at every stage of coal mine operation. It is demonstrated that the use of high-performance equipment in the production and development areas requires more precise filtration equations used when assessing coal mine methane hazard. A mathematical model of pressure field of non-associated methane in the edge area of the coal seam has been justified. The model is based on one-dimensional hyperbolic equation and takes into consideration final rate of pressure distribution in the seam. Trends in gas exchange between mined-out spaces of high methane- and CO 2 -concentration mines with the earth surface have been refined in order to ensure environmental safety of underworked territories.
