The basic physical concepts underlying the theories of anomalous transport in magnetic confinement devices are reviewed. Anomalous transport is a consequence of electric and/or magnetic fluctuations driven by various linear and/or nonlinear instability mechanisms. The latter saturate by inducing a relaxation of the profiles towards a marginally stable state or/and by 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, a non exhaustive list of which is given. A rough estimate of the nuclear heating power required to balance the anomalous losses in the International Tokamak Experimental Reactor (HER) is calculated on the basis of the electrostatic drift wave instability model.