Focusing and sorting cells and particles utilizing microfluidic phenomena have been flourishing areas of development in recent years. These processes are largely beneficial in biomedical applications and fundamental studies of cell biology as they provide cost-effective and point-of-care miniaturized diagnostic devices and rare cell enrichment techniques. Due to inherent problems of isolation methods based on the biomarkers and antigens, separation approaches exploiting physical characteristics of cells of interest, such as size, deformability, and electric and magnetic properties, have gained currency in many medical assays. Here, we present an overview of the cell/particle sorting techniques by harnessing intrinsic hydrodynamic effects in microchannels. Our emphasis is on the underlying fluid dynamical mechanisms causing cross stream migration of objects in shear and vortical flows. We also highlight the advantages and drawbacks of each method in terms of throughput, separation efficiency, and cell viability. Finally, we discuss the future research areas for extending the scope of hydrodynamic mechanisms and exploring new physical directions for microfluidic applications.