Recent advances in technology and refinement of available computational resources paved the way for the extensive use of computers to model and simulate complex real-world problems difficult to solve analytically. The appeal of simulations lies in the ability to predict the significance of a change to the system under study. The simulated results can be of great benefit in predicting various behaviors, such as the wind pattern in a particular region, the ability of a material to withstand a dynamic load, or even the behavior of a workpiece under a particular type of machining. This paper deals with the mathematical modeling and simulation techniques used in abrasive-based machining processes such as abrasive flow machining (AFM), magnetic-based finishing processes, i.e., magnetic abrasive finishing (MAF) process, magnetorheological finishing (MRF) process, and ball-end type magnetorheological finishing process (BEMRF). The paper also aims to highlight the advances and obstacles associated with these techniques and their applications in flow machining. This study contributes the better understanding by examining the available modeling and simulation techniques such as Molecular Dynamic Simulation (MDS), Computational Fluid Dynamics (CFD), Finite Element Method (FEM), Discrete Element Method (DEM), Multivariable Regression Analysis (MVRA), Artificial Neural Network (ANN), Response Surface Analysis (RSA), Stochastic Modeling and Simulation by Data Dependent System (DDS). Among these methods, CFD and FEM can be performed with the available commercial software, while DEM and MDS performed using the computer programming-based platform, i.e., "LAMMPS Molecular Dynamics Simulator," or C, C++, or Python programming, and these methods seem more promising techniques for modeling and simulation of loose abrasive-based machining processes. The other four methods (MVRA, ANN, RSA, and DDS) are experimental and based on statistical approaches that can be used for mathematical modeling of loose abrasive-based machining processes. Additionally, it suggests areas for further investigation and offers a priceless bibliography of earlier studies on the modeling and simulation techniques for abrasive-based machining processes. Researchers studying mathematical modeling of various micro- and nanofinishing techniques for different applications may find this review article to be of great help
