This book is intended to present the interested reader with the knowledge required to design and operate microfluidic systems that make use of non-Newtonian fluids, and in particular of viscoelastic fluids. It will offer valuable information on the prediction of the corresponding flow characteristics and the onset of non-Newtonian flow instabilities, which can be used to improve mixing in micro-scale processes, with the corresponding benefits in throughput. It will also include a discussion on the capabilities and the limits of operation of the micro-systems where improved mixing and flow instabilities are undesirable as in micro-rheology setups. The book will provide knowledge on state of the art experimental methods for the characterization of non-Newtonian properties of the fluids, and will discuss and present specific numerical techniques to deal with flows of elastic fluids, namely under high-Weissenberg number flow conditions. A particular focus will be given to strong extensional flows, either for rheological characterization, or for single molecule studies or deformation of drops or cells. Recent advances on optimization techniques to design efficient microfluidic devices will also be presented, including the basics of the methodology and applications in the development of microfluidic extensional rheometers, microfluidic rectifiers or micromixing elements.