The last few years have seen a decrease in technical failures thanks to technological development and enhanced protection and security measures that have made the systems more reliable. However, it is not possible to talk about the reliability of the system without addressing the failure rate of all its components, including humans. The contribution of the human factor in the dynamics of accidents is very high, both statistically and in terms of severity, and it is estimated that human factor errors amount to 60-90% of all accidents, while only the rest is attributed to technical defects. It is clear that incidents are the most obvious errors in industrial systems, but a single failure can seriously reduce the performance of the system in terms of productivity and efficiency. In fact, human error has a direct impact on productivity because errors affect the rejection rate of products, thus increasing production costs, and reduced revenues in later sales. Therefore, there is a need to assess human reliability to reduce the likely causes of errors. The aim of this paper was to study the currently available methods for human reliability analysis (HRA), quantitative first generation (such as THERP and HEART methods), and qualitative second generation (such as ATHEANA and CREAM methods). These methods aim to estimate the probability of human errors in industrial systems, for a specific operation, in a specific time interval and in a specific context. The mentioned methods strive to describe the complex mechanisms that lie behind certain human actions that are subject to error, in a more or less simlified way, using certain models.