For many centuries avalanches have been a serious threat to the inhabitants of the Alps. In the second half of the last century, the first attempts were made in Switzerland to fight this danger actively. After World War II - as a result of increasing tourism and building activities - our Institute started regular communication of avalanche warnings to the public. As snow is an extremely complex material - changing its properties continuously with time, often over ranges of several orders of magnitude - applied methods were (and still are) a mixture of empirical knowledge and deterministic reasoning, the latter always enhanced by the progress of physical snow research. In the 'seventies attempts were started in different countries to replace the empirical knowledge as far as possible by statistical or deterministic-statistical models.
The following contributions give some insight into different approaches to the problem in question, confining the discussion to work done in our Institute or in collaboration with other institutions. The apparent inhomogeneity of the paper should not be taken in a negative sense; it demonstrates the need for different approaches to a complex problem.