Wind energy farms are moving into deeper and more remote waters to benefit from availability of more space for the installation of wind turbines as well as higher wind speed for the production of electricity. Wind farm asset managers must ensure availability of adequate power supply as well as reliability of wind turbines throughout their lifetime. The operating conditions in deep water environments often change very rapidly and, therefore the decision metrics used in different phases of a wind energy project's lifecycle will have to be updated on a very frequent basis, to guarantee higher wind energy system reliability levels. For this reason, there is a crucial need for the wind energy industry to develop advanced computational tools/techniques that are capable of modelling the possible scenarios in (near) real-time and provide a prompt response to any changes in operational/environmental conditions. Bayesian network (BN) is a popular machine learning (ML) method used for system modelling and decision-making under uncertainty. This paper provides a systematic review and evaluation of existing research on the use of BN models in the wind energy sector. To conduct this literature review, all relevant databases from inception to date were searched, and a total of 70 sources (including journal publications, conference proceedings, PhD dissertations, industry reports, best practice documents and software user guides) which met the inclusion criteria were identified, excluding references used in other sections of the text for discussion. Our review findings reveal that the applications of BNs in the wind energy industry are quite diverse, ranging from wind power and weather forecasting to risk management, fault diagnosis and prognosis, structural analysis, reliability assessment, and maintenance planning and updating. Furthermore, a number of case studies are presented to illustrate the applicability of BNs in practice. Although the paper details information applicable to the wind energy industry, knowledge can be transferred to many other sectors.