Analogical thinking is significant in problem solving. This chapter discusses the use of diagrams as aids to analogical problem solving when the two analogous problems are in very different semantic domains. Two functions of diagrams are proposed. The first is to aid in the encoding of problem structure. The second function is to serve as a retrieval cue for relevant prior information in memory. The chapter describes the transfer paradigm used to study problem solving by analogy. The major transfer problem used to study analogical problem solving is Duncker's radiation problem, which involves finding a way to use rays to destroy a stomach tumor without destroying the surrounding healthy tissue. High intensity rays can destroy the tumor, but can also destroy the tissue; on the other hand low intensity rays can destroy neither healthy tissue nor the tumor. The primary story analog to solve the radiation problem involves a military situation in which a general wishes to lead an attack of his entire army against a dictator located in a centrally-located fortress.