Fraction and decimal arithmetic are crucial for later mathematics achievement and for ability to succeed in many professions. Unfortunately, these capabilities pose large difficulties for many children and adults, and students' proficiency in them has shown little sign of improvement over the past three decades. To summarize what is known about fraction and decimal arithmetic and to stimulate greater amounts of research in the area, we devoted this review to analyzing why learning fraction and decimal arithmetic is so difficult. We identify and discuss two types of difficulties: (1) Difficulties that are inherent to fraction and decimal arithmetic, and (2) Culturally contingent sources that could be reduced by improved instruction and prior knowledge of learners. We conclude the review by discussing commonalities among three interventions that have helped children overcome the difficulties of mastering fraction and decimal arithmetic. [This article was published in the "Developmental Review," v38 p201-221 Dec 2015.]