The main goal of mathematics education is to train individuals as have reasoning and connection skills, well-adjusted with their environment, productive and can solve problems that faced throughout in their lives. Modeling competencies take place in the center of this goal. When the literature examined, it can be seen that there are many studies on developing and assessing mathematical modeling competencies and it is seen that the adopted approaches are different from each other. However, systematic classifications of the relevant approaches, how it can be improve and how mathematical modeling can be integrated into learning environment are not dealt with in detail in the literature. In this study, studies on developing and assessing mathematical modeling competencies were examined and studies were classified by analyzing comparative in terms of integration mathematical modeling on the learning environment approaches and mathematical modeling competencies assessment approaches. The classifications set out in this study depending on the approaches and examples are thought to shed light on the discussions and studies on developing and assessing mathematical modeling competencies.