Cyber ranges are often used to enhance the cybersecurity posture of a company by training relevant skills. These environments are traditionally used to host exercises that simulate cybersecurity scenarios, improve the cybersecurity skills of employees and enhance the security of networks and processes. By using digital twins, it is possible to organise more targeted cyber range trainings to companies operating in the critical infrastructure sector. Especially in this sector it is important to consider the cybersecurity of these environments themselves as they often may handle companyspecific confidential information. This study presents several cybersecurity related threats and challenges that cyber ranges may face during different phases of use. Cyber threats may be exposed to the actual systems that the ranges are meant to protect if these issues are not taken into consideration and mitigated. Malicious attackers may use the information in the cyber ranges to learn the weaknesses in the actual system. We approach the subject by reviewing the relevant literature, which is currently very limited especially when looking at the cybersecurity issues of cyber ranges. We divide the subject into the different phases of cyber range development and use, and also discuss relevant cloud security issues. Finally, we present actions to mitigate the identified cybersecurity threats and issues in cyber ranges when using them for training and awareness activities.