Faults are inevitable in building energy systems, such as heating, ventilation, air conditioning and refrigeration systems. With the increasing utilization of these systems, their fault detection and diagnosis has become more significant for maintaining their operation and performance. The rapid development of data analytics has led to fault detection and diagnosis using data-based algorithms considering building intelligence. Feature engineering, which focuses on generating near minimum and optimal model inputs from the original dataset, is a fundamental technique to balance efficiency and accuracy of fault detection and diagnosis models. The generated inputs are fault features which ensures a better description of fault operations owing to their stronger fault indicative capability than original data. However, since most feature engineering research has been implemented alongside the development of data-based algorithms, most studies fail to effectively distinguish and understand their roles in fault detection and diagnosis models. To fill this research gap, this study presented the problems and mechanisms associated with feature engineering, comprehensively reviewed about 200 papers on the topic of feature engineering for heating, ventilation, air conditioning and refrigeration system fault detection and diagnosis tasks over the past 15 years. Firstly, feature engineering studies are divided according to their feature-generation technique, into manual and automated techniques. Next, feature engineering studies are analysed in terms of data type, system type, fault type, operation statue, methods and fault features. The desirable characteristics of feature engineering works are then discussed in terms of their capability of rapidly generating indicative, decoupled, interpretable and new fault features to enhance fault detection and diagnosis accuracy; the efficiency, reliability and robustness of feature engineering process; the mutual adaptability between feature engineering and fault detection and diagnosis; and their widespread applicability for more fault types and system operations. The challenges affecting feature engineering studies are discussed in terms of data volume, data diversity and quality, along with the performance evaluation of feature engineering with respect to feature engineering algorithms, fault detection and diagnosis models, fault features and online application constraints. Future work should aim to design a hybrid, heuristic, robust and automated feature engineering strategy under the guidance of expert knowledge and practical application constraints that consider the relationships between fault-related features and real-time fault impacts with energy consumption, occupants' thermal comfort, etc.