Safety systems, i.e., systems whose malfunction can result in catastrophic consequences, are usually designed with redundancy in mind to reach high levels of reliability. However, Common Cause Failures (CCF), i.e., single failure events affecting multiple components or functions in a system, can threaten the desired reliability. To solve this problem, practitioners must use proven methods, such as those recommended by standards, to support CCF quantification. In particular, the β-factor model has become the de-facto model since the safety standard IEC 61508 considers it. As such standard applies to all industries, practitioners must figure out the industrial-specific implementation procedures. In this paper, we conducted a systematic literature review to understand how the β-factor model has been used in practice. As a result, we found 20 different models, which are industry/project-specific extensions of the first β-factor model proposed for the nuclear sector. We further classified those models by considering how the β-factor is estimated, and the level of redundancy support. Tool support for the models and their industrial use are also outlined. Finally, we present a discussion that covers the implication of our findings. Our study targets practitioners and researchers interested in using current β-factor models or evolving new ones for specific project needs.