Scale symmetry is an important concept in quantum and statistical physics. It arises at fixed points of the renormalisation group, often alongside full conformal symmetry, and implies that theories are massless with correlation functions given by universal numbers. New phenomena arise when scale symmetry is broken spontaneously, leading to a Goldstone boson, the dilaton, and the appearance of a mass scale that is not determined by the fundamental parameters of the theory. In this talk, I discuss scalar, fermionic, and Yukawa theories in three dimensions, each with lines of strongly-coupled conformal fixed points that terminate with spontaneous scale symmetry breaking. Interrelations between models, dualities, and aspects of dilaton physics are worked out from first principles. Further implications for CFTs and model building are indicated.