Fraction and decimal arithmetic pose large difficulties for many children and adults. This is a serious problem, because proficiency with these skills is crucial for learning more advanced mathematics and science and for success in many occupations. This review identifies two main classes of difficulties that underlie poor understanding of rational number arithmetic: inherent and culturally contingent. Inherent sources of difficulty are ones that are imposed by the task of learning rational number arithmetic, such as complex relations among fraction arithmetic operations, and that are present for all learners. Culturally contingent sources of difficulty are ones that vary among cultures, such as teacher understanding of rational numbers, and that lead to poorer learning among students in some places than others. We conclude by discussing interventions that can improve learning of rational number arithmetic. [This research was supported in part by the Siegler Center for Innovative Learning and Advanced Technology Center, Beijing Normal University. At time of submission to ERIC, this article was in press with "Current Directions in Psychological Science."]