This review discusses the diffusion model for light transport in tissues and its applications in medical diagnostics. It highlights the use of diffuse light for measuring tissue hemodynamics, including the quantitative assessment of oxy- and deoxy-hemoglobin concentrations and blood flow. The theoretical basis for near-infrared spectroscopy (NIRS) and diffuse optical tomography (DOT) is developed, along with an overview of diffuse correlation spectroscopy (DCS), a technique that measures blood flow by analyzing temporal correlation functions of diffusing light. Essential instrumentation and examples of brain and breast functional imaging and monitoring are provided to illustrate the practical applications of these new tissue diagnostics. The review also delves into the theoretical background, including the photon diffusion formalism, source types, diffuse photon density waves, solutions in infinite and homogeneous turbid media, boundary conditions, Green's function solutions, and spectroscopy for determining tissue chromophore concentrations. Additionally, it covers the differential pathlength approach and the dynamic light scattering techniques used in DCS.This review discusses the diffusion model for light transport in tissues and its applications in medical diagnostics. It highlights the use of diffuse light for measuring tissue hemodynamics, including the quantitative assessment of oxy- and deoxy-hemoglobin concentrations and blood flow. The theoretical basis for near-infrared spectroscopy (NIRS) and diffuse optical tomography (DOT) is developed, along with an overview of diffuse correlation spectroscopy (DCS), a technique that measures blood flow by analyzing temporal correlation functions of diffusing light. Essential instrumentation and examples of brain and breast functional imaging and monitoring are provided to illustrate the practical applications of these new tissue diagnostics. The review also delves into the theoretical background, including the photon diffusion formalism, source types, diffuse photon density waves, solutions in infinite and homogeneous turbid media, boundary conditions, Green's function solutions, and spectroscopy for determining tissue chromophore concentrations. Additionally, it covers the differential pathlength approach and the dynamic light scattering techniques used in DCS.