Summarizes problem-solving theories in 3 areas: traditional learning, cognitive-Gestalt approaches, and more recent computer and mathematical models of problem solving. Recent empirical studies are categorized according to the type of behavior elicited by the particular problem-solving task. Anagram, "insight," water-jar, and arithmetic problems are considered to be solved by covert trial-and-error behavior. Switch-light, classification, probability-learning, and numerous "miscellaneous" tasks are approached by overt trial-and-error behavior. (3 p. ref.)