This book presents a comprehensive overview of fluid mechanical, thermal and physico-chemical aspects of drop-surface interactions. Basic physical mechanisms pertaining to free-surface flow phenomena characteristic of drop impact on solid and liquid surfaces are explained emphasizing the importance of scaling. Moreover, physico-chemical fundamentals relating to a forced spreading of complex solutions, analytical tools for calculating compressibility effects, and heat transfer and phase change phenomena occurring during solidification and evaporation processes, respectively, are introduced in detail. Finally, numerical approaches particularly suited for modeling drop-surface interactions are consisely surveyed with a particular emphasis on boundary integral methods and Navier-Stokes algorithms (volume of fluid, level set and front tracking algorithms). The book is closed by contributions to a workshop on Drop-Surface Interactions held at the International Centre of Mechanical Sciences.