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This paper provides a review of the underlying theory of the Barkhausen effect in magnetic materials. The paper contains throughout many of the equations that are commonly used in the mathematical description of this phenomenon. A new contribution in this paper is the examination of how Barkhausen effect can be described in the presence of hysteresis using a hysteretic-stochastic process model. Although the Barkhausen effect has been known for many years its quantitative description has been rather slow in emerging. One reason for this is that as a result of its random nature the experimental observations are not completely reproducible and this means that the description is necessarily complicated by this fact. Nevertheless a mathematical description is possible and the Barkhausen effect does contain useful information about the details of the magnetization processes occuring on a microscopic scale, both from domain wall motion and domain rotation. This information can only be utilized in conjunction with a model description that can be used to interpret the results. The domain wall motion can be described in terms of two limiting models — flexible domain wall motion and rigid domain wall motion. Both give reasonably tractable mathematical solutions, and each has reversible and irreversible components. Domain rotation also has two limiting models — reversible and irreversible rotation, depending on the anisotropy and the magnitude of the angle of rotation. After having discussed the underlying physical description of the main mechanisms the paper proceeds to describe stochastic process models for Barkhausen effect, in particular recent work by Bertotti et al. It is then shown how the stochastic model can be generalized to include the effects of hysteresis. Finally the paper discusses measurement of the Barkhausen effect and how this can be used for the evaluation of stress and microstructure at the surface of a magnetic material.