The demand for precise separation of particles, cells, and other biological matter has significantly increased in recent years, leading to heightened scientific interest in this topic. More recently, due to advances in computational techniques and hardware, numerical simulations have been used to guide the design of separation devices. In this article, we establish the theoretical basis governing fluid flow and particle separation and then summarize the computational work performed in the field of particle and cell separation in the last five years with an emphasis on magnetic, dielectric, and acoustic methods. Nearly 70 articles are being reviewed and categorized depending on the type of material separated, fluid medium, software used, and experimental validation, with a brief description of some of the most notable results. Finally, further conclusions, future guidelines, and suggestions for potential improvement are highlighted.