The metal-based additive manufacturing (MAM) processes have great potential in wide industrial applications, for their capabilities in building dense metal parts with complex geometry and internal characteristics. However, various defects in the MAM process greatly affect the precision, mechanical properties and repeatability of final parts. These defects limit its application as a reliable manufacturing process, especially in the aerospace and medical industries where high quality and reliability are essential. MAM process monitoring provides a technical basis for avoiding and eliminating defects to improve the build quality. Based on of the nature of the MAM build defects, this article conducts a thorough investigation of monitoring methods, and proposes a machine learning (ML) framework for process condition monitoring. According to the structure of ML models, they are divided into shallow ML-based and deep learning-based methods. The state-of-the-art ML monitoring approaches, as well as the advantages and disadvantages of their algorithmic implementations, are discussed. Finally, the prospects of ML based process monitoring researches are summarized and advised.