By the end of the last century, organizations began to realize that the application of project management was more a matter of need rather than choice. Although project management has spread to almost all sectors of the economy, it is noticeable that a large number of IT and ICT companies have benefited significantly from its implementation. Due to the growing popularity of software development in this innovative age, the need for a number of methodologies to adequately manage such complex projects has emerged. One of the most popular choices in these industries is Scrum Framework. The Scrum framework represents the way a project is executed with certain role artifacts and activities that ultimately result in great value for the project. The purpose of this paper is to examine the challenges that arise when using the Scrum framework for software project development. Therefore, in the theoretical part, the concept of agile project management is explained, as well as its methodologies and frameworks, and the Scrum framework is explained in more detail. Also, the specifics of software development project management are clarified, more precisely its trends, determinants and challenges. The empirical part of the paper presents research on the challenges of software development project management using the Scrum framework for agile project management in Croatian IT and ICT companies. The research was conducted with a survey questionnaire examining 39 main challenges with Scrum. It was sent to the mentioned companies and received at least one response (per company) from different relevant persons within the project team. The results of the research showed that, despite the many advantages of the Scrum framework, companies still face a significant number of challenges across the spectrum. Despite this, organizations still choose the Scrum framework and deliver successful software.