Microfluidic techniques are effective tools for precise manipulation of particles and cells whose enrichment and separation is crucial for a wide range of applications in biology medicine and chemistry. Recently lateral particle migration induced by the intrinsic hydrodynamic effects in microchannels such as inertia and elasticity has shown its promise for high-throughput and label-free particle manipulation. The particle migration can be engineered to realize the controllable focusing and separation of particles based on a difference in size. The widespread use of inertial and viscoelastic microfluidics depends on the understanding of hydrodynamic effects on particle motion. This review will summarize the progress in the fundamental mechanisms and key applications of inertial and viscoelastic particle manipulation.