Our first book on the applications of density functional theory in compositional hydrodynamics was published in Russian in 2009. Since then we observed a steady rise of interest to our approach. Also during the last four years we acquired much more experience and obtained many new numerical results. The present book is an update to the state-of-the-art in density functional hydrodynamics. It is written in English to be accessible to wider audience. This book is essentially about various multiphase hydrodynamic problems studied in the frame of the density functional method. This approach is a logical extension of classical thermodynamics and continuous media theory. The derivation of the governing equations is presented, and the consistency with both classical and quantum statistical mechanics is demonstrated. Several explicit density functionals are used to describe different types of continuous media. Among them there are models for equilibrium and nonequilibrium two- and three-phase compositional mixtures, mixtures with surfactants, and mixtures with mobile elastic bodies. Numerous numerical simulation examples are presented to demonstrate the capabilities of the density functional method. Among them there are very simple problems such as modeling of contact angle and capillary pressure in two- and three-phase cases. There are also more complex scenarios with capillary waves, moving contact lines, changing topology of interfaces, multiphase flows in complex geometries, instabilities, liquid-liquid and liquid-solid phase transitions, surfactant effects, thermocapillary effects, flows with moving elastic bodies, and two-phase turbulence. Being an overview of the results accumulated over the last almost 20 years, the book can be a good starting point in studying the density functional theory in compositional hydrodynamics. The book is intended for PhD students, academic and industrial researchers interested in modeling complex behavior of compositional fluids.