Arithmetic word problems are a staple in mathematical curricula yet give individuals of all ages difficulty. Successful word problem solving requires translating the problem into a symbolic arithmetic format. However, the linguistic component may make problem solving more complex and increase cognitive load, specifically the processes that interact with reading comprehension, such as working memory and inhibitory control. This comprehensive review examines the overall relationship between comprehension and word problem success, and how different linguistic factors and related cognitive processes impact word problem performance. We highlight the importance of cognitive processes by proposing models that spotlight the roles of inhibitory control and working memory in word problem performance. Furthermore, we emphasize the need for researchers and practitioners to rethink the strategies that are utilized in the development of word problem-solving skills.