Using methods of integrability, enormous progress has been done in calculating the spectrum of operators in N=4 Super Yang-Mills theory as well as of energies of strings. I will discuss advances in finding the spectrum of the Konishi operator, the simplest nontrivial operator of finite size, which is already a hard problem. A further mathematical problem is to prove integrability. I will discuss the algebraic objects appearing in the AdS/CFT correspondence, namely Yangians, and also show how they are related to the spectral equations.