The operational safety of large-scale dynamic systems in complex and constantly changing environments is paramount. Therefore, safety assessment techniques are essential to help avoid accidents and ensure safe operation. This paper first reviews different definitions and perspectives on safety assessment for dynamic systems. In particular, we formulate the online safety assessment (OSA) problem to attract more attention from researchers. Then, the current state of research on system safety assessment is presented, including commonly used methods and application objects. The safety assessment methods in the literature are categorized into offline and online approaches. However, offline approaches are primarily knowledge-based and cannot be applied in real time. Meanwhile, research on data-driven OSA methods is still in its early stages and faces various challenges. These challenges are summarized as human-in-the-loop, domain knowledge integration, complex data characteristics, and open environments. Finally, this paper provides insight into promising directions for the further development of OSA.