This book is a unique collection of high-level papers devoted to fundamental topics in mathematical fluid mechanics and their applications, mostly in connection with the scientific work of Giovanni Paolo Galdi. The contributions are mainly centered on the study of the basic properties of the Navier-Stokes equations, including existence, uniqueness, regularity, and stability of solutions. Related models describing non-Newtonian flows, turbulence, and fluid-structure interactions are also addressed. The results are analytical, numerical and experimental in nature, making the book particularly appealing to a vast readership encompassing mathematicians, engineers and physicists. The diversity of the topics, in addition to the different approaches, will provide readers a global and up-to-date overview of both the latest findings on the subject and of the salient open questions.