In recent years increasing theoretical attention has been directed towards the maximally supersymmetic theories, because of their unique properties and richness of beautiful structures. In four dimensions  N=4 super-Yang-Mills and N=8 supergravity are paramount examples of such theories, owing much of their fame due to their hidden stringy nature, revealed in the AdS/CFT duality and M-theory low-energy limit, respectively. Similarly, in recent years there has been a veritable revolution in the field of perturbative calculations, leading to new efficient methods for computing scattering amplitudes using the old ideas of unitarity and analyticity of the S-matrix.  Besides their phenomenological applications, the new methods are excellent tools in the perturbative studies of the maximally supersymmetric theories, shedding new light on the AdS/CFT duality and on the possibility of N=8 supergravity being the first example of an ultraviolet finite gravity theory with point-like particles. \par In this talk I will discuss the process of computing multiloop scattering amplitudes in N=4 super-Yang-Mills and N=8 supergravity.  The calculations are based on the unitarity method, which together with the simple structure of the maximally supersymmetric theories allows one to probe these theories to high loop orders. In particular, I will discuss the structure of the four-point amplitudes, which are calculated up to four loops. By analyzing the potential ultraviolet divergences of the amplitudes we obtain that N=8 supergravity is finite through four loops. Even more remarkably, we show that N=8 supergravity obeys the same power counting bound as the all-order finite N=4 super-Yang-Mills theory, providing direct evidence of the claimed ultraviolet finiteness of N=8 supergravity.