Laser metal additive manufacturing (LMAM) is a significant part of the advanced manufacturing industry. The technology enables the production of complex parts via layer-by-layer deposition through robust bonding mechanisms. Despite the inherent advantages of additive technology, the quality control of its products remains the challenge to increase the applicability of the AM parts and products as complex physical processes occur at the melt pool (MP) where laser and metal interact. There are many variables in LMAM that impact the final part quality, and many scholars have investigated how the individual variable affects the part quality. The contribution this review makes is to assess how process parameters affect process signatures (derived from in situ techniques) and how these in turn affect part quality. By focussing on the connection across process parameters, process signatures, and part quality, the review aims to systematically tackle the complexity of the LMAM process and thus provide insight into online diagnostic of quality estimation. This paper starts with common part quality issues and briefly reviews process parameters to part quality correlations. As a vital step to link the process parameters and part quality, different in situ monitoring techniques and their acquired data are summarised. The correlations between the important factors affecting the quality of the additive process are systematically reviewed. These correlations include parameter-signature, signature-quality, and parameter-signature-quality correlations. Linking process parameters and part quality through the process signatures is highly desirable. These correlations bring opportunities to design a more comprehensive feedback controller to improve the repeatability and reliability of LMAM systems. Results found through the investigation of disconnected factors contribute to building a holistic understanding of LMAM.