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The goal of the report is to show new trends and results of the Mathematical morphology of landscape. The mathematical morphology of landscape is a scientific branch studying both numerical regularities (laws) of landscape patterns and methods of their mathematical analysis. The basic concept of the mathematical morphology is a mathematical model of a landscape pattern. Mathematical models of landscape patterns comprise a set of equations describing behavior of general numerical characteristics of a landscape pattern of a certain genesis. The theory of random processes is a base of the mathematical morphology of landscape. Thus we can make a conclusion that at present we have got the base of the mathematical morphology of landscape as a set mathematical models of landscape patterns (mosaics). Techniques of the mathematical morphology of landscape can be used in different branches of geosciences. The new and promising trends of the mathematical morphology of landscapes include: Natural risk assessment for engineering constructions, Representation of processes in the landscape pattern, to be more precise, quantitative assessment of territory dynamics by its quantitative features without repeated observation, Analysis of dynamic balance in development of landscape patterns, Development of regional subdivisions, such as mathematical morphology of landscapes in the permofrost zone.