Chemical process industries (CPI) are usually home to a large number of complex systems and components required for various operations involving hazardous chemicals. The intense operating conditions and complex interactions between the systems make the chemical plants vulnerable to accidents. Quotidian incidents and mishaps can lead to catastrophic incidents. Thus, the area of risk assessment and reliability analysis in CPI has been of much interest to the research community. The complexity of processes in CPI demands a risk assessment tool that can adapt itself to the dynamic environment and can efficiently model the functional and sequential dependencies between the components and the effects of external factors, component degradation, and variation in operating conditions. The risk assessment tool must have applicability during the operational lifetime of the system to serve as a platform for decision making and risk management. The unavailability of empirical data for some variables is another pertinent issue in risk analysis and reliability assessment in CPI. Analysts often have to work with subjective information such as expert opinion. Bayesian statistical methods based on the Bayes theorem are considered by many to be an effective tool to address the above-mentioned issues. These methods are based on the subjective interpretation of probability that helps to model the epistemic uncertainties and easily propagates them through complex system models. The methods provide a formal systematic way to incorporate subjective information into calculations. The inherent updating property accoutres these methods with the ability to deal with real-time changes. The opponents, however, point out that the methods produce high overconfidence and randomness in computed answers. In the last two decades, an increased interest can be seen in the research community toward the use of Bayesian methods in risk assessment. This paper presents a comprehensive literature review of the application of Bayesian methods through Bayesian parameter estimation techniques and Bayesian updating procedures in process industries. Both these techniques have been extensively used in various aspects of risk analysis, which are very pertinent in CPI. The purpose of the study is to produce an effective reference guide for scholars interested in applying Bayesian techniques to risk and reliability assessment in CPI.