We will discuss a construction of classes of N=1 superconformal theories labeled by punctured Riemann surfaces. Degenerations of the surfaces correspond, in some cases, to weak coupling limits. Different classes are labeled by two integers (n,k). The k=1 case coincides with SU(n) N=2

For the space of N=1 theories to be complete in an appropriate sense we find it necessary to conjecture existence of new N=1 strongly coupled SCFTs. 

These SCFTs when coupled to additional matter can be related by dualities to gauge theories. As our main example we will discuss in more detail the SU(2) case with k=2 using the supersymmetric index as our analysis tool.  The index of theories in classes with k>1 can be constructed using eigenfunctions of elliptic quantum mechanical models generalizing the Ruijsenaars-Schneider integrable model appearing when k=1.