The Bayesian model (BM) of category-based induction provides a unified computable framework for explaining the experimental phenomena (including the premise-conclusion similarity effect, the premise diversity effect, the premise monotonic effect and the premise-conclusion asymmetric effect, etc.) in category-based induction. Within this framework, the inductive reasoning in different contexts (such as induction about the generic biological properties or the causally transmitted properties) requires the constraint of different kinds of prior knowledge. Different kinds of prior knowledge can be represented by different kinds of category structures (i.e., the relationship between categories) and the corresponding stochastic process (i.e., the distribution of features/ properties in the category structure). Thus, BM can get the prior probability distributions for the Bayesian inference engine, and finally, the strength of an inductive argument can be calculated. As compared to the similarity coverage model (SCM) and feature-based inductive model (FBIM), BM can reflect the interaction of categories and properties, and has a clear mathematical basis, and also shows a better ability of prediction. This paper firstly reviews the research history and state of the art of the BM, and summarizes the process of computational cognitive modeling using BM. Secondly, BM is compared with the other models, and then the advantages and disadvantages of the BM are commented in details. Finally, some potential research directions are proposed: 1) further improving the ability of BM to deal with the common sense knowledge (e.g., the predatory behavior of animal), which may help to expand its application scope; 2) further increasing the power of BM to handle multiple objects and features/properties (if we learn that the animal A has the property X, what’s the possibility of the animal B having the property Y?); 3) that in combination with other methodologies (e.g., functional magnetic resonance imaging (fMRI) and computational linguistics, such as corpora), BM may improve its practical availability and reasoning abilities.