Fixed points are crucial in understanding the RG flow of quantum field theories. The conformal bootstrap has proved a wonderful tool in determining the properties of CFTs at fixed points but tends to require guidance in terms of what symmetries to impose and what is the spectrum of relevant operators. Here I review what can be said in general by using the time honoured epsilon expansion. Although qualitatively this is not nowadays the most efficient method it provides qualitative information about possible fixed points. Finding fixed points which cannot be linked to the epsilon expansion could provide a clue to non Lagrangian theories.

The application of the AdS/CFT correspondence in the calculation of four point functions for chiral primary operators in the large N limit for maximal superconformal gauge theories is reviewed. It is shown how the results satisfy certain constraints, motivated by our understanding from string theory of the spectrum of operators in the large N limit, which allow a construction of the four point function for any half BPS chiral primary operator at large N.