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The two concepts in the title stand for two distinct quantum phenomena whose relation to one another is not obvious although they often occur together. Moreover, there is not a unique concept of superfluidity. In the talk I shall first comment on these general issues and then discuss a simple model involving a tunable random potential where some precise statements can be rigorously proved. The latter is joint work with M.Könenberg, T. Moser and R. Seiringer.