The phenomenology of transport in magnetically confined plasmas is briefly described and the basic physical concepts underlying the theories of both anomalous and neoclassical transport are reviewed. Anomalous transport is a consequence of supra-thermal electric and magnetic fluctuations driven unstable by various mechanisms. The excited modes saturate by inducing a relaxation of the profiles towards the marginally stable state and via nonlinear coupling of the various modes. Specific theoretical models are described, together with their successes and drawbacks in the light of observed characteristics of plasma confinement. An estimate of the nuclear heating power required to balance the anomalous losses in the International Tokamak Experimental Reactor (ITER) is obtained on the basis of the electrostatic drift wave instability model. Large-scale gyrokinetic turbulence simulations and various “theoretical” transport models are discussed. Recent improvements of neoclassical theory, required in the vicinity of transport barriers, are described.