Abstract Heuristic search is a general problem-solving method. Some heuristic search algorithms, like the well-known A? algorithm, are domainindependent, in the sense that their knowledge of the problem at-hand is limited to the (1) initial state, (2) state transition operators and their costs, (3) goal-test function, and (4) black-box heuristic function that estimates the value of a state. Prominent examples are A? and Weighted A? . Other heuristic search algorithms are domaindependent, that is, customized to solve problems from a specific domain. A well-known example is conflict-directed A? , which is specifically designed to solve model-based diagnosis problems. In this paper, we review our recent advancements in both domain-independent and domain-dependent heuristic search, and outline several challenging open questions