:We review various notions of self-similar fractal compact sets such as Hutchinson’s, Kigami’s or Kamiyama’s, and see which way most of them can be reached through an inceasing sequence of approximating compact sets. This leads to the definition of a similarity scheme, then of the associated similarity functor, both in the classical and the non commutative workframe. We finally define a self-similar C*-algebra as a fixed point of the similarity functor. We show then how, to any similarity scheme, is associated a projective sequence of C*-algebras, which heuristically tends to self-similarity. We show how it is possible to define a natural projective limit to such a sequence and we provide easy criteria for this limit arising without loss of information. Which will provide a self-similar C*-algebra naturally associated with the similarity scheme we started with. Examples will include new examples of self-similar sets and C*-algebras. This is a joint work in progress with Fabio Cipriani, Daniele Guido and Tommaso Isola.