In recent years, metal additive manufacturing (AM) and particularly the laser powder bed fusion (LPBF) process have substantially grown in popularity in industrial applications due to its unique ability to produce a wide variety of components with complex geometry. The LPBF process is now an integral part of digital manufacturing and the industry 4.0 concept. However, a considerable amount of residual stress and deformation induced by the fast and intense heating/cooling cycle as well as phase change in each layer are still some important technical barriers in the LPBF process, giving rise to increasing inaccuracy and structural failure in some cases. Developing an efficient physics-based simulation model capable of predicting the induced residual stresses is, thus, of paramount importance to build parts with minimal distortion in a wide range of applications, while avoiding expensive and time-consuming experimental procedures. The simulation model also is efficiently utilized to investigate the effect of process parameters, material, and geometry on the development and redesign of parts. In the last decade, multi-scale process modeling frameworks have been developed to predict the residual stress and deformation cost-effectively in the parts fabricated by LPBF. The purpose of this survey is to systematically provide an in-depth overview of the inherent strain modeling approach with a focus more on the methodology development, highlighting the positive outcomes and limitations of recent investigations, followed by presenting potential future work to optimize this technique.