Colloidal systems under flow are ubiquitous in nature and technology, whether it is the transport of proteins and enzymes in biological systems or the flow of surfactants in enhanced oil recovery. Such microrheological systems are also highly intriguing from a purely scientific point of view due to the intricate interplay between the solute and solvent particles. To better understand the physical properties of these complex systems and to assist the design of microfluidic devices, we performed extensive simulations of both rigid and soft colloidal particles under flow. This computational approach allows for systematic control over the system parameters while also providing microscopic insight. In this presentation, selected systems will be discussed to give an overview of the possibilities and challenges in this field. For example, microfluidic channels can be used to distinguish polymers based on their topology, such as linear, dendritic or ring-shaped macromolecules. Furthermore, non-linear flow effects such as inertia or viscoelasticity can be exploited to control the lateral motion of dispersed particles. Flow can also be used to enhance the growth as well as the breakup of colloidal aggregates, depending on the applied flow strength.