In a book that focuses on advances in mathematics education, it is essential that there is a chapter that focus on problem solving, because problem solving has been one of the prominent phenomenon in the development of mathematics teaching and learning. This chapter by English and Sriraman is a seminal piece of work because it provides a critical and thoughtful review of the history of problem solving that avoids idealising and valorising the value and impact it has had in mathematics education without diminishing its enduring importance. After affirming the crucial nature of problem solving for mathematics education and simultaneously discussing the disappointing limited influence it has had, the authors have provided avenues for further development. In particular, the focus on mathematical modelling as an integral part of the mathematics curriculum was valuable as it provided well-considered direction for research. This research-based discussion is timely and provides an important discussion of the topic that will ground future research and development. A broad range of research reports have been discussed and the extensive reference list is indicative of the comprehensive nature of the chapter.