We analyze the current experimental and theoretical research about the magnetization (Barkhausen) noise in magnetic thin films. We observe that, in respect to three-dimensional systems, the situation is much more complicated, and many details still have to be analyzed and understood. In particular, the critical exponents must be correctly analyzed when compared with the theoretical predictions. We observe, for instance, that the easured magnetization steps in optical measurements do not actually correspond to the avalanche size, as claimed, but to a different quantity having a different critical exponent. We also observe as the lack of a significative demagnetizing field does not assure to have a stationary Barkhausen signal, which again implies a different set of exponents. For comparison, we report in detail all the possible theoretical values of the critical exponents calculated for a single DW model.