The frequentist and bayesian approaches to scientific inference are discussed. The Bayesian approach is discussed in the cases in which prior information is available, prior information is available under certain hypotheses, prior information is vague and there is no prior information. The most usual methods in animal breeding (Selection index, BLUP, ML, REML) are presented under the hypotheses of both schools of inference, and their properties are examined in both cases. Bayesian prediction of genetic values and genetic parameters are presented. Finally, the frequentist and bayesian approaches are compared from an ontological and practical point of view. Some problems for which the Bayesian methods offer solutions that are not found by using frequentist methods are exposed.