Studies of transport in fusion plasmas using perturbations of an equilibrium state are reviewed. Essential differences between steady-state and perturbative transport studies are pointed out. Important transport issues that can be addressed with perturbative experiments are identified as: (i) Are the transport relations linear (or nearly so)? (ii) What are the dominant dependences on plasma parameters; can they be understood from theory? (iii) Are there significant off-diagonal terms in the transport matrix? If so, how important are these for global confinement? (iv) Do the data obtained with perturbative experiments indicate that tokamak performance can be optimized along lines different from those presently explored? The theoretical framework for perturbative transport experiments is given. It is shown that perturbative experiments yield transport coefficients that are essentially different from the steady-state transport coefficients. In particular, when transport can be described by a transport matrix with off-diagonal elements, a perturbative experiment yields (one or more of) the eigenvalues of the matrix. In contrast, the coefficients obtained by steady-state analysis are linear combinations of the matrix coefficients, with the actual values of the various gradients as multipliers. Hence, the outcome of a steady-state transport evaluation depends on the actual values of the gradients, whereas a perturbative experiment measures the underlying transport matrix. Experimental perturbation techniques and techniques for data analysis are reviewed. Perturbations include the sawtooth instability, oscillatory gas feed, modulated power input, pellet injection etc. Data analysis techniques range from the time-to-peak analysis employed in sawtooth pulse propagation through Fourier or Laplace transforms, to direct numerical modelling. A review of the most important sources of systematic error is given.