Untimely machinery breakdown will incur significant losses, especially to the manufacturing company as it affects the production rates. During operation, machines generate vibrations and there are unwanted vibrations that will disrupt the machine system, which results in faults such as imbalance, wear, and misalignment. Thus, vibration analysis has become an effective method to monitor the health and performance of the machine. The vibration signatures of the machines contain important information regarding the machine condition such as the source of failure and its severity. Operators are also provided with an early warning for scheduled maintenance. Numerous approaches for analyzing the vibration data of machinery have been proposed over the years, and each approach has its characteristics, advantages, and disadvantages. This manuscript presents a systematic review of up-to-date vibration analysis for machine monitoring and diagnosis. It involves data acquisition (instrument applied such as analyzer and sensors), feature extraction, and fault recognition techniques using artificial intelligence (AI). Several research questions (RQs) are aimed to be answered in this manuscript. A combination of time domain statistical features and deep learning approaches is expected to be widely applied in the future, where fault features can be automatically extracted from the raw vibration signals. The presence of various sensors and communication devices in the emerging smart machines will present a new and huge challenge in vibration monitoring and diagnosing.