Health monitoring in rotatory machinery is a process of developing a mechanism to determine its state of deterioration. It involves analysing the presence of damage, locating the fault, determining the severity of the problem, and calculating the amount of time that the machine can still be used effectively by making use of signal processing methods. The journey started to repair when the machine fails and progressed to the modern era, which involves the use of advanced sensors to capture data and conduct on-line signal processing methods to extract relevant features. By seamlessly integrating advanced smart sensing, data collection, and intelligent algorithms, modern technologies have transformed the landscape of condition-based maintenance for rotary machinery, bridging the gap between fundamental understanding and practical engineering applications. In this review paper, first, the roadmap of the condition-based maintenance (CBM) journey for rotary machinery is briefly introduced. Then, CBM task techniques are reviewed in the context of manual identification of defects, applying artificial intelligence (AI) model to identify the defect in the rotary machinery, and AI to carry out defect prognosis and determine the remaining useful life. Finally, the challenges, and issues of signal processing methods to detect faults in rotary machinery, and remedies to overcome such challenges are deeply discussed and future research directions are identified to ensure safe operation for rotary machinery.