The methods and results of the theory of homogenization and their applications to flow and transport in porous media are discussed in this book. It offers a systematic and rigorous treatment of upscaling procedures related to physical modeling for porous media on micro-, meso-, and macro-scales. The chapters are devoted to percolation, Newtonian and non-Newtonian phenomena, two-phase flow, miscible displacement, and thermal and elastic effects. Detailed studies of micro-structure systems and computational results for dual-porosity models are presented. This book will be of interest to readers who want to learn the principal underlying ideas and concepts of modern mathematical theory, including the most recently obtained results and applications. Mathematicians, soil physicists, geo-hydrologists, chemical engineers, and researchers working in oil reservoir simulation or in the environmental sciences will find this book of particular interest.