This paper is divided into two parts. In the first part (sections 2 and 3), I will describe briefly how advances in artificial intelligence (AI) in the 1970s led to the crucial problem of handling uncertainty, and how attempts to solve this problem led in turn to the emergence of the new theory of Bayesian networks. I will try to focus in this historical account on the key ideas and will not give a full account of the technical details. Then, in the second part (section 4), I will consider the implications of these new results for the long-standing controversy between Bayesians and non-Bayesians.