1 Introduction -- 1.1 Basic Idea -- 1.2 First Examples -- 1.3 Diffusion in Periodic Media -- 1.4 Formal Derivation of Darcy's Law -- 1.5 Formal Derivation of a Distributed Microstructure Model -- 1.6 Remarks on Networks of Resistors, Capillary Tubes, and Cracks -- 2 Percolation Models for Porous Media -- 2.1 Fundamentals of Percolation Theory -- 2.2 Exponent Inequalities for Random Flow and Resistor Networks -- 2.3 Critical Path Analysis in Highly Disordered Porous and Conducting Media -- 3 One-Phase Newtonian Flow -- 3.1 Derivation of Darcy's Law -- 3.2 Inertia Effects -- 3.3 Derivation of Brinkman's Law -- 3.4 Double Permeability -- 3.5 On the Transmission Conditions at the Contact Interface between a Porous Medium and a Free Fluid -- 4 Non-Newtonian Flow -- 4.1 Introduction -- 4.2 Equations Governing Creeping Flow of a Quasi-Newtonian Fluid -- 4.3 Description of a Periodic s-Geometry, Construction of the Restriction Operator, and Review of the Results of Two-Scale Convergence in Lq-Spaces -- 4.4 Statement of the Principal Results -- 4.5 Inertia Effects for Non-Newtonian Flows through Porous Media -- 4.6 Proof of the Uniqueness Theorems -- 4.7 Uniform A Priori Estimates -- 4.8 Proof of Theorem A -- 4.9 Proof of Theorem B -- 4.10 Conclusion -- 5 Two-Phase Flow -- 5.1 Derivation of the Generalized Nonlinear Darcy Law -- 5.2 Upscaling Two-Phase Flow Characteristics in a Heterogeneous Reservoir with Capillary Forces (Finite Peclet Number) -- 5.3 Upscaling Two-Phase Flow Characteristics in a Heterogeneous Core, Neglecting Capillary Effects (Infinite Peclet Number) -- 5.4 The Double-Porosity Model of Immiscible Two-Phase Flow -- 6 Miscible Displacement -- 6.1 Introduction -- 6.2 Upscaling from the Micro-to the Mesoscale -- 6.3 Upscaling from the Meso-to the Macroscale -- 6.4 Discussion -- 7 Thermal Flow -- 7.1 Introduction -- 7.2 Basic Equations -- 7.3 Natural Convection in a Bounded Domain -- 7.4 Natural Convection in a Horizontal Porous Layer -- 7.5 Mixed Convection in a Horizontal Porous Layer -- 7.6 Thermal Boundary Layer Approximation -- 7.7 Conclusion -- 8 Poroelastic Media -- 8.1 Acoustics of an Empty Porous Medium -- 8.2 A Priori Estimates for a Saturated Porous Medium -- 8.3 Local Description of a Saturated Porous Medium -- 8.4 Acoustics of a Fluid in a Rigid Porous Medium -- 8.5 Diphasic Macroscopic Behavior -- 8.6 Monophasic Elastic Macroscopic Behavior -- 8.7 Monophasic Viscoelastic Macroscopic Behavior -- 8.8 Acoustics of Double-Porosity Media -- 8.9 Conclusion -- 9 Microstructure Models of Porous Media -- 9.1 Introduction -- 9.2 Parallel Flow Models -- 9.3 Distributed Microstructure Models -- 9.4 A Variational Formulation -- 9.5 Remarks -- 10 Computational Aspects of Dual-Porosity Models -- 10.1 Single-Phase Flow -- 10.2 Two-Phase Flow -- 10.3 Some Computational Results -- A Mathematical Approaches and Methods -- A.1.1 F-Convergence -- A.1.2 G-Convergence -- A.1.3 H-Convergence -- A.2 The Energy Method -- A.2.1 Setting of a Model Problem -- A.2.2 Proof of the Results -- A.3 Two-Scale Convergence -- A.3.1 A Brief Presentation -- A.3.2 Statement of the Principal Results -- A.3.3 Application to a Model Problem -- A.4 Iterated Homogenization -- B Mathematical Symbols and Definitions -- B.1 List of Symbols -- B.2 Function Spaces -- B.2.1 Macroscopic Function Spaces -- B.2.2 Micro-and Mesoscopic Function Spaces -- B.2.3 Two-Scale Function Spaces -- B.2.4 Time-Dependent Function Spaces -- C References.