This study provides a comprehensive overview of challenges and advancements in vibration analysis for machinery operations under non-stationary and non-linear conditions. Non-stationary operation in machinery occurs when operating conditions such as speed, load, and environmental factors change over time. This results in dynamic behaviours that cause fluctuating vibration signals, making fault detection challenging with traditional methods that assume stationary conditions. The paper provides foundational insights and clear concepts on essential topics, including non-stationary operations in rotary machinery , vibration signals in non-stationary operations, cycle-stationary analysis, and the quantification of non-stationary operations. Further advancing, this paper explores the challenges and methodologies in condition-based monitoring for non-stationary machinery operations, focusing on the analysis of vibrational signals. It examines the complexities of working with non-stationary and cyclo -stationary signals and the limitations of traditional signal processing techniques . The study reviews classical time–frequency and advanced signal-processing methods, highlighting their advantages, drawbacks, and applicability in real-world scenarios. Additionally, it addresses the identification of defects across varying operational speeds, identifying gaps in current methodologies and suggesting potential avenues for future research. The paper also emphasizes the importance of transfer learning in non-stationary environments, analyzing various approaches and their effectiveness in improving monitoring performance. Lastly, it discusses the development of expertise and adoption pathways for AI-based predictive maintenance , offering insights into the practical integration of advanced technologies in industrial settings.