The growing complexity and interconnectivity of modern systems have made the proactive identification and mitigation of vulnerabilities increasingly challenging. DTs, which offer dynamic and real-time virtual representations of physical systems, have emerged as a potential solution to enhance cybersecurity. However, several significant challenges exist, including the integration of DTs with existing cybersecurity frameworks and the effective use of DTs to detect and mitigate zero-day vulnerabilities. In this study, we conduct a systematic literature review to explore these challenges by addressing four key research questions. Our findings reveal critical challenges and open research problems associated with the implementation of DTs for cybersecurity. These insights are essential for advancing the security of complex systems, paving the way toward building resilient and secure cyber-infrastructures, enabling real-time assessment, effective remediation actions and cyber perception on emerging threats.