This report, prepared for and published by the Mathematical Association of America's Committee on the Teaching of Undergraduate Mathematics, includes a description of the state of the art on problem solving, lists available resources, and makes recommendations regarding the place of problem solving in the college curriculum and ways to teach it. The report recommends (1) an approach to teaching mathematics that fosters an alert and questioning attitude in students and that actively engages them in the process of doing mathematics, (2) a series of problem-solving courses at various levels of sophistication as regular offerings in the standard college curriculu, and (3) a series of texts for problem-solving courses at all levels to be developed and disseminated. Specific suggestions are given on how to teach problem solving, especially pertaining to the role of the teacher and ways of organizing the class. Some typical problems and class discussions are provided. Then follows an extensive annotated bibliography of problem-solving resources, with characterizations of the type of course for which each appears most appropriate, its focus or subject matter, and its level. Journals, books, and articles are listed separately. Finally, the problem-solving questionnaire and responses are briefly presented. (MNS)