Microfluidic devices have been widely used since 1990s for diverse manipulations of particles (a general term of beads, cells, vesicles, drops, etc.) in a variety of applications. Compared to the active manipulation via an externally imposed force field, the passive manipulation of particles exploits the flow-induced intrinsic lift and/or drag to control particle motion with several advantages. Along this direction, inertial microfluidics has received tremendous interest in the past decade due to its capability to handle a large volume of samples at a high throughput. This inertial lift-based approach in Newtonian fluids, however, becomes ineffective and even fails for small particles and/or at low flow rates. Recent studies have demonstrated the potential of elastic lift in non-Newtonian fluids for manipulating particles with a much smaller size and over a much wider range of flow rates. The aim of this article is to provide an overview of the various passive manipulations, including focusing, separation, washing and stretching, of particles that have thus far been demonstrated in non-Newtonian microfluidics. (C) 2017 Elsevier Inc. All rights reserved.