User behavior is widely acknowledged as a crucial part of cybersecurity, and training is the most commonly suggested way of ensuring secure behavior. However, an open challenge is to get users to engage with such training to a high enough extent. Consequently, this paper provides research into user acceptance of cybersecurity training. User acceptance can be understood from a socio-technical perspective and depends on the training itself, the organization where it is deployed, and the user expected to engage with it. A structured literature review is conducted to review previous research on cybersecurity training acceptance using a social-technical approach. The paper contributes with an overview of how user acceptance has been researched in the three social-technical dimensions and with what results. The review shows that previous research mostly focused on how the training method itself affects user acceptance, while research focusing on organizational or user-related dimensions is more scarce. Consequently, the paper calls for further research on the organizational aspects of user acceptance of cybersecurity training and how user acceptance can differ between user groups.