The Standard Model extended with non-renormalisable operators is increasingly becoming THE theory of the elementary particles and their interactions. A large part of current and future research is devoted to test this theory to the best possible accuracy. To this aim, though, substantial knowledge on its quantum structure is needed, both for theoretical reasons (constraints on the basis of relativity+quantum mechanics) and experimental ones (combine data gathered at very different energies). In this talk I will discuss the progress made over the years in this respect, with particular emphasis on major obstacles.