The purpose of this article is to analyze the most popular maturity models in order to identify their strengths and weaknesses. Research conducted by international project management communities such as Software Engineering Institute (SEI), Project Management Institute (PMI), International Project Management Association (IPMA), Office of Government Commerce (OGC) and International Organization for Standardization (ISO) showed that organizations with high managerial maturity are more likely to achieve their planned project goals than those that do not identify and standardize their best management practices. This circumstance has encouraged scientists from all over the world to start developing various models that can measure and evaluate managerial maturity in projects. Nowadays, the variety of models created has led to considerable difficulty in understanding the strengths and weaknesses of each model. To solve this problem, the article authors conducted a critical analysis to identify the strengths and weaknesses of the most popular project management maturity models. The results obtained will be of interest to project managers, members of project teams, heads of organizations, project offices and everyone involved in the development of project activities. Based on the analysis, it was found that the most developed maturity models are based on international codes of knowledge of project management. Most maturity models ignore the presence of structural and infrastructural elements, such as a workplace, the necessary equipment and software, the availability of professional standards, instructions, regulations, etc. It was also revealed that there are no processes for assessing the effectiveness and efficiency of using the best practices in the maturity models.