Abstract In this paper, we identify a number of topics relevant for the improvement and development of discrete estimation of distribution algorithms. Focusing on the role of probability distributions and factorizations in estimation of distribution algorithms, we present a survey of current challenges where further research must provide answers that extend the potential and applicability of these algorithms. In each case we state the research topic and elaborate on the reasons that make it relevant for estimation of distribution algorithms. In some cases current work or possible alternatives for the solution of the problem are discussed.