In this paper we focus on some of the findings of the science education research community in the area of representations and problem solving. Problem solving depends on the construction and manipulation of mental models (internal representations) in the mind. A large knowledge base (declarative, procedural, strategic, situational, and schematic knowledge), working memory capacity, and metacognitive skills play an important role in the construction and manipulation of mental models, and therefore in problem solving. In this point, applications of research for classroom practice is considered. Finally, external representations are discussed. Using multiple representations when solving problems is beneficial for students, representational formats of problems affect student performance, and the utilization of representational learning strategies can lead to substantial improvements in problem solving.