  Analogies have had and continue to have an important role in the development
of theoretical physics. They may start from similarities of physical concepts
followed by similarities in the mathematical formalization or it may be a
purely mathematical aspect to suggest the development of analogous physical
concepts. More often a subtle non obvious interplay between these levels is
involved. In this paper I will discuss two cases sufficiently intricate to
illustrate some ways of how analogies work. The first topic is the introduction
of spontaneous symmetry breaking in particle physics. The second one is the use
of the renormalization group in the theory of critical phenomena and its
statistical interpretation.
