The rise of hardware-level security threats, such as side-channel attacks, hardware Trojans, and firmware vulnerabilities, demands advanced detection mechanisms that are more intelligent and adaptive. Traditional methods often fall short in addressing the complexity and evasiveness of modern attacks, driving increased interest in machine learning-based solutions. Among these, Transformer models, widely recognized for their success in natural language processing and computer vision, have gained traction in the security domain due to their ability to model complex dependencies, offering enhanced capabilities in identifying vulnerabilities, detecting anomalies, and reinforcing system integrity. This survey provides a comprehensive review of recent advancements on the use of Transformers in hardware security, examining their application across key areas such as side-channel analysis, hardware Trojan detection, vulnerability classification, device fingerprinting, and firmware security. Furthermore, we discuss the practical challenges of applying Transformers to secure hardware systems, and highlight opportunities and future research directions that position them as a foundation for next-generation hardware-assisted security. These insights pave the way for deeper integration of AI-driven techniques into hardware security frameworks, enabling more resilient and intelligent defenses.