  In this thesis we discuss supersymmetric gauge theories, focusing on exact
results achieved using methods of integrability. For the larger portion of the
thesis we study the N=4 super Yang-Mills theory in the planar limit, a
recurring topic being the Konishi anomalous dimension, which is roughly the
analogue for the mass of the proton in quantum chromodynamics. The N=4
supersymmetric Yang-Mills theory is known to be integrable in the planar limit,
which opens up a wealth of techniques one can employ in order to find results
in this limit valid at any value of the coupling. We begin with perturbation
theory where the integrability of the theory first manifests itself. Here we
showcase the first exact result, the so-called slope function, which is the
linear small spin expansion coefficient of the generalized Konishi anomalous
dimension. We then move on to exact results mainly achieved using the novel
quantum spectral curve approach, the method allowing one to find scaling
dimensions of operators at arbitrary values of the coupling. As an example we
find the second coefficient in the small spin expansion after the slope, which
we call the curvature function. This allows us to extract non-trivial
information about the Konishi operator. Methods of integrability are also
applicable to other supersymmetric gauge theories such as ABJM, which in fact
shares many similarities with N=4 super Yang-Mills. We briefly review these
parallel developments in the last chapter of the thesis.
