Research on the transfer of problem solving between knowledge domains is reviewed. It is concluded that instructional and programming studies do not provide evidence for any essential contribution of the computer to problem solving. Instead, it is recommended that studies focus on the cognitive processes that are required for farther transfer and how these processes can be supported by instruction for students who fail to transfer. Two types of cognitive processes presumed to be active during problem solving are discussed: 1) The selecting of structural features of problem representations and 2) the connecting of features in two or more domains during transfer. The connecting process is discussed in depth and two types of connections are hypothesized, first, horizontal connections between knowledge structures in the form of analogies, and second, vertical connections within knowledge structures in the form of rule-example chains. It is suggested that analogies promote domain-general transfer because they provide horizontal connections between similar knowledge structures in different domains and induce rules that enlarge and extend the links between knowledge. Research focused on the use of analogies in problem solving is offered to support instructional prescriptions intended to facilitate domain-general problem solving.