The article highlights the importance of the cost management for the success of projects and organizations, respectively. Through the comparative approach it is demonstrated that cost is one of the key elements of modern project management methodologies. We consider that the cost management represents the set of processes that ensure the planning, estimating, budgeting, financing, managing, and controlling costs so that the project can be completed within the approved budget. The analysis of the evolution of the content of the project cost management is presented by the comparative-evolutionary analysis of this topic in more advanced editions of Project Management Body of Knowledge and another methodologies which are known and used internationally. The paper presents the processes that make up the cost management proposed in PMBOK's last edition and the author support the opinion that they, in general, contribute to the elaborating and ensurance the project realization within the budgets limits. The analysis of processes in project cost management has allowed the generalization of some ways of improvement of this domain. Finally, there are exposed some trends and emerging practices in project cost management.