In this paper Carlo Sempi makes an interesting survey on the theory of probabilistic normed spaces. The survey describes clearly which has been the evolution of this theory in the framework of probabilistic metric spaces with special attention to the original definition (1962) of A. N. Sherstnev and to the new approach (1993) of C. Alsina, B. Schweizer and A. Sklar. Then a detailed overview of all contributions made to the theory is given. This complete description gives to the present paper a great interest for those interested in the theory. Moreover key open problems are stated.