This report presents a view on the current state and perspective of mathematical modeling of global and regional biosphere and climate changes under anthropogenic inputs. A spatial model of carbon cycle in the "Atmosphere -- Plants -- Soil" system is described, and the impact of industrial CO2 emissions, deforestation and soil erosion on the dynamics of the "Atmosphere -- Terrestrial Ecosystems -- Ocean" system is analyzed. The countries' carbon dioxide budget of 1995 is estimated. Consequences of several scenarios of the implementation of the Kyoto Protocol to the UN Framework Convention on Climate change are discussed. The stability of the biosphere and climate are treated from the point of view of the biosphere's ability to compensate anthropogenic inputs. In this context, the issue of the validity of the Le Chatellier principle in the biosphere is considered.