Due to the potential to miniaturize, integrate and automate sample preparation and analysis, lab-on-chips have witnessed a massive growth in research and development in the past two decades. The ability to accurately control and manipulate particles and fluid flow in microsystems is one of the main challenges of microfluidics to reach these goals. Inertial microfluidics, which exploits the flow non-linearities induced in finite Reynolds number flow regime, has been studied and employed as a platform for passive and high-throughput control of particles in microchannels in recent years. However, due to the complexity of the fluid dynamics associated with these systems much of the rich underlying physics is yet to be understood. This dissertation unravels parts of the unexplored physical phenomena occurring in inertial flow regime and reports new strategies for controlling and manipulating fluid flow and microparticles. We first provide a theoretical background of the underlying physics of non-linear microfluidic systems, especially inertial microfluidics. We then discuss the effects of particles on fluid in an inertial flow regime. The novel phenomenon of "particle-induced convection" is introduced where moving particles act as dynamic sites to induce net secondary flows inside microchannels which can be used for heat and mass transfer. Finally, we introduce a novel technique to induce strong net secondary flows by positioning simple microstructures (i.e. cylindrical pillars) inside straight microchannels. We make use of the inertial flow deformations associated with the flow around a library of single cylindrical pillars at eight positions within a microfluidic channel as fundamental operations for more complex fluid manipulations. Since transformations for each basic pillar location provide a deterministic mapping of fluid elements from upstream to downstream of a pillar, we can sequentially arrange pillars to apply the associated nested maps and therefore program complex fluid structures without additional numerical simulation, inducing order rather than chaos in microflows. Consequently, functions composed of multiple pillars can be hierarchically assembled to execute practical programs. To show the range of capabilities we demonstrate programs to sculpt the cross-sectional shape of a stream into complex geometries (such as various concavity polygons, closed rings, and inclined lines), move and split a fluid stream, transfer particles from a stream, and separate particles by size.