The purpose of this review is to introduce the reader to the concepts of delay and probability discounting as well as the major empirical findings to emerge from research with humans on these concepts. First, we review a seminal discounting study by Rachlin, Raineri, and Cross (1991) as well as an influential extension of this study by Madden, Petry, Badger, and Bickel (1997). In doing so, we describe the general procedure used for assessing discounting and the resulting form of the obtained discounting functions. With this as background, we review additional empirical findings that have emerged over the last 20 years, by addressing issues such as time consistency and preference reversals, magnitude effects, and the gain-loss asymmetry. Finally, we conclude with a discussion of more recent developments and their implications for the future of this growing area. (Contains 3 figures and 9 footnotes.)