Interest in children's concepts of chance and probability has been prompted by several questions. Assuming that the development of a concept of chance and probability is influenced by experience, what are the conditions that bring it about? What are its precursors? Is it acquired all at once, or is it acquired gradually over a relatively long period of time? At what age is its development complete? Does every mature adult have a similarly functioning concept of chance, or are there individual differences? If so, how are they to be explained? To what extent is a concept of chance a result of formal instruction in school? What kinds of training are likely to improve upon immature or deficient concepts of chance or probability? When making probability judgments, is there a optimum strategy that can be said to be correct in each type of situation, or is there a variety of strategies more or less adequate or appropriate? To what extent is performance in a probability setting controlled by the reinforcing consequences of previous outcomes? What is the relationship between chance and probability concepts, on the one hand, and the development of linguistic ability to articulate them, on the other? In what ways are various probability tasks alike, and how do they differ? What makes some tasks seem harder than others? What is the relationship between the development of concepts of chance or probability and cognitive development in general? These do not seem to be trivial questions. Indeed, many of them have been addressed in published research reports and monographs. The purpose of this chapter is to review procedures that have been devised to investigate some of these questions and to evaluate the conclusions that have tentatively been drawn.