The manipulation of cells and particles suspended in viscoelastic fluids in microchannels has drawn increasing attention, in part due to the ability for single-stream three-dimensional focusing in simple channel geometries. Improvement in the understanding of non-Newtonian effects on particle dynamics has led to expanding exploration of focusing and sorting particles and cells using viscoelastic microfluidics. Multiple factors, such as the driving forces arising from fluid elasticity and inertia, the effect of fluid rheology, the physical properties of particles and cells, and channel geometry, actively interact and compete together to govern the intricate migration behavior of particles and cells in microchannels. Here, we review the viscoelastic fluid physics and the hydrodynamic forces in such flows and identify three pairs of competing forces/effects that collectively govern viscoelastic migration. We discuss migration dynamics, focusing positions, numerical simulations, and recent progress in viscoelastic microfluidic applications as well as the remaining challenges. Finally, we hope that an improved understanding of viscoelastic flows in microfluidics can lead to increased sophistication of microfluidic platforms in clinical diagnostics and biomedical research. Modeling microscale manipulation of biofluidsInsights into the dynamic behavior of biological fluids on the microscale are enabling more efficient analysis of cells, bacteria, and other small biological particles for research and clinical diagnostics. Blood, saliva and other biofluids have viscoelastic properties, which means that they exhibit both viscous and elastic behaviors depending on the forces to which they are subjected. These properties shape the migration behaviors of suspended bioparticles in unique ways. Jian Zhou and Ian Papautsky of the University of Illinois at Chicago have reviewed current progress in understanding the migration behaviors in such fluids within microfluidic devices. The authors discuss design principles that have enabled the development of microfluidic systems capable of separating and purifying cells, bacteria, and small vesicles from highly heterogeneous biological specimens, and highlight future challenges that need to be addressed.