Tokamak plasmas are, at present, the most studied objects in controlled thermonuclear fusion research. The basic concept of these devices relies on externally induced currents which serve the twofold purpose of heating the plasma and creating an appropriate magnetic field structure for confinement. A detailed knowledge of the current density distributions and the dependencies on the operational conditions are important for both the theoretical understanding and the practical improvement of Tokamaks. The experimental techniques for measuring the current density profile or the associated magnetic fields within the plasma are reviewed. After a brief description of the equilibrium magnetic field configuration in toroidal geometry and a short account of indirect and passive diagnostic methods, an assessment is made of the currently available techniques with respect to the state of development and the obtained results.