Recent years have witnessed an elevated trend in using miniaturized and labon- a-chip systems in biomedical devices due to numerous advantages including minimal sample/reagent consumption, portability, and superior performance. One of the key challenges within these microsystems is to precisely manipulate and order bio-particles. Various techniques have been introduced to accomplish this mission. Inertial microfluidics enables lateral migration of particles and cells in laminar flow regime due to the velocity gradient effect in moderate Reynolds number. Moreover, viscoelastic fluids exploit intrinsic elastic property of the fluids to transfer particles and cells across laminar ow streamlines. Both methods utilize inherent properties of fluids alleviating any external force field inducer. This dissertation elucidates inertial and viscoelastic effects on particles and cells motion and investigates some unexplored migration behaviors. For inertial migration study, a new fabrication method termed tape'n roll is introduced enabling to study migration in both 2D and 3D structures. To better unravel the covert mechanism of migration, computational model is applied. For viscoelastic behavior study, focusing of particles inside three different viscoelastic fluids in a straight glass capillary tube is scrutinized through optical system and image processing.