The main physical aspects and the theoretical description of stochastic domain wall dynamics in soft magnetic materials are reviewed. The intrinsically random nature of domain wall motion results in the Barkhausen effect, which exibits scaling properties at low magnetization rates and 1/f power spectra. It is shown that the Barkhausen signal ν, as well as the size Δx and the duration Δu of jumps follow distributions of the form ν−α, Δx−β, Δu−γ, with α=1−c, β=3/2−c/2, γ=2–c, where c is a dimensionless parameter proportional to the applied field rate. These results are analytically calculated by means of a stochastic differential equation for the domain wall dynamics in a random perturbed medium with brownian properties and then compared to experiments. The Barkhausen signal is found to be related to a random Cantor dust with fractal dimension D=1−c, from which the scaling exponents are calculated using simple properties of fractal geometry. Fractal dimension Δ of the signal v is also studied using four different methods of calculation, giving Δ≈1.5, independent of the method used and of the parameter c. The stochastic model is analyzed in detail in order to clarify if the shown properties can be interpreted as manifestations of self-organized criticality in magnetic systems.