Particles suspended in flow through small pipes are known to migrate across streamlines of the fluid flow due to a phenomena known as inertial lift. This effect causes the particles to focus towards specific locations within the cross-section. This is exploited in the field of microfluidics for a range of applications that utilise particle focusing and/or separation, one such example being the separation of circulating tumour cells. In this talk I will discuss some of the modelling, computation and analysis I have done on particle migration in curved microfluidic ducts. The secondary vortices that develop in curved duct flow adds significant complexity to the problem. Using a clever decomposition of the flow we have made significant progress in understanding how the effects of inertial lift and secondary vortices interact to produce a wide range of particle dynamics. I will review some of the more interesting results from this research and outline the directions I hope to take this work going forwards.