Due to complex dependencies between multiple layers and components of emerging cyber-physical systems, security and vulnerability of such systems have become a major challenge in recent years. In this regard, game theory, a powerful tool for modeling strategic interactions between multiple decision makers with conflicting objectives, offers a natural paradigm to address the security-related issues arising in these systems. While there exists substantial amount of work in modeling and analyzing security problems using game-theoretic techniques, most of the existing literature in this area focuses on static game models, ignoring the dynamic nature of interactions between the main players (defenders vs. attackers). In this paper, we focus only on dynamic game analysis of cyber-physical security problems and provide a general overview of the existing results and recent advances based on application domains. We also discuss several limitations of the existing models and identify several hitherto unaddressed directions for future research.