Diffuse-interface methods in fluid mechanics are reviewed, focusing on their application to interfacial phenomena. These models are particularly effective for situations where the physical phenomena involve length scales comparable to the interfacial region thickness, such as near-critical phenomena, small-scale flows near contact lines, and large interface deformations. The models are formulated for single-component and binary fluids, addressing issues like sharp-interface analyses, computational approaches, and fully-miscible fluid models. The diffuse-interface approach replaces the sharp interface with a diffuse region, allowing for a more accurate description of interfacial phenomena. The models are based on a capillary stress tensor that accounts for the distribution of stresses within the interfacial region. The models have been successfully applied to various fluid dynamics problems, including critical point scaling, shear flows, capillary waves, moving contact lines, internal waves, droplet breakup, spinodal decomposition, and mixing. The diffuse-interface models are also compared to sharp-interface models, showing how they can approach the free-boundary formulation in the sharp-interface limit. The models have been used to study a wide range of fluid dynamics problems, including thermocapillary flows, nucleation, and wave-breaking and sloshing. The diffuse-interface approach provides a more accurate and flexible framework for modeling complex interfacial phenomena in fluid mechanics.Diffuse-interface methods in fluid mechanics are reviewed, focusing on their application to interfacial phenomena. These models are particularly effective for situations where the physical phenomena involve length scales comparable to the interfacial region thickness, such as near-critical phenomena, small-scale flows near contact lines, and large interface deformations. The models are formulated for single-component and binary fluids, addressing issues like sharp-interface analyses, computational approaches, and fully-miscible fluid models. The diffuse-interface approach replaces the sharp interface with a diffuse region, allowing for a more accurate description of interfacial phenomena. The models are based on a capillary stress tensor that accounts for the distribution of stresses within the interfacial region. The models have been successfully applied to various fluid dynamics problems, including critical point scaling, shear flows, capillary waves, moving contact lines, internal waves, droplet breakup, spinodal decomposition, and mixing. The diffuse-interface models are also compared to sharp-interface models, showing how they can approach the free-boundary formulation in the sharp-interface limit. The models have been used to study a wide range of fluid dynamics problems, including thermocapillary flows, nucleation, and wave-breaking and sloshing. The diffuse-interface approach provides a more accurate and flexible framework for modeling complex interfacial phenomena in fluid mechanics.