Chapter 1 takes a look at a general set of equations of motion and constitutive equations of various rheologically complex fluids. In Chapter 2, general forms of equations of motion in a curvilinear coordinate system are discussed. After considering the order-of-magnitude of the general equations of motion, a set of reduced equations of motion for magnetic and electro-rheological fluids is derived. Chapter 3 presents basic flows of selected non-Newtonian fluids in rectilinear channels. These flows constitute the basis of the considerations presented in the next chapters. Chapter 4 deals with hydrodynamics in porous media with applications to various structures including also fractal structures and some biological structures. Chapter 5 presents the methods of solutions of reduced equations of flow between surfaces of revolution. Methods of averaged inertia, self similarity, small parameter, asymptotic solutions and moments are considered. Majority of these methods is illustrated by respective examples. Chapter 6 focuses on the flows of selected non-Newtonian fluids between non-rotating surfaces of revolution. A considerable part of the text is dedicated to the flows of electrorheological fluids. Chapter 7 addresses the flows of selected non-Newtonian fluids between rotating surfaces of revolution. First, the flow of a viscoelastic fluid is considered, next – a generalized second grade fluid and then two flows of polar fluids (couple-stress and micropolar). Chapter 8 explores the application of rheology in tribology; otherwise speaking: the application of different non-Newtonian fluids in lubrication of curved thrust bearings with rotating pins and squeeze films. The working bearing surfaces were considered as non-porous and porous, smooth or rough; the lubricants flows were considered without or with inertia effects.