The objective of this book is several-fold. Firstly, it collects and describes the most significant experiments that do not find explanation in the classical Newtonian (Navier–Stokes) theory. Then, it introduces some of the most commonly used models of non-Newtonian fluid, including Reiner–Rivlin, power law, simple fluid, and Oldroyd-B models. These models are explored through an updated mathematical investigation, with particular regard to the well-posedness of the corresponding boundary and initial-boundary value problems. Finally, it presents a rigorous mathematical explanation of the relevant experiments.