This review discusses the diffusion model for light transport in tissues and its medical applications, particularly in measuring tissue hemodynamics and functional imaging. Diffuse optics is useful for quantifying oxy- and deoxy-hemoglobin concentrations and blood flow. The theoretical basis for near-infrared (NIRS) and diffuse optical spectroscopy (DOS) is developed, along with the basic elements of diffuse optical tomography (DOT). Diffuse correlation spectroscopy (DCS) is also discussed, which uses temporal correlation functions of diffusing light to measure blood flow. Essential instrumentation and representative results from brain and breast imaging are presented. The diffusion model is based on the radiation transport equation (RTE), which describes light propagation in tissues. The RTE is approximated using the $P_{N}$ method, with the $P_{1}$ approximation being particularly useful for nearly isotropic light. The diffusion model allows for the separation of scattering and absorption effects, enabling the measurement of tissue properties such as hemoglobin, water, and lipid concentrations. The model is validated in various biological tissues and has been used to measure blood flow, oxygen extraction rates, and other physiological parameters. The review outlines the theoretical background of diffuse optics, including the photon diffusion formalism, source types, and boundary conditions. It discusses the use of frequency-domain and time-domain solutions to the diffusion equation, as well as the application of Green's functions for solving the diffusion equation in various geometries. The review also covers the determination of tissue chromophore concentrations using spectroscopy, with a focus on the optimal selection of wavelengths for accurate measurements. The differential pathlength approach is introduced for measuring changes in chromophore concentrations and scattering properties. The review concludes with a discussion of diffuse correlation spectroscopy (DCS), which measures blood flow by analyzing the temporal correlation of diffusing light. DCS has been validated in various biological tissues and has shown promise for continuous non-invasive monitoring of physiological parameters. The review highlights the versatility of diffuse optics in a wide range of applications, including functional imaging and monitoring of tissue properties.This review discusses the diffusion model for light transport in tissues and its medical applications, particularly in measuring tissue hemodynamics and functional imaging. Diffuse optics is useful for quantifying oxy- and deoxy-hemoglobin concentrations and blood flow. The theoretical basis for near-infrared (NIRS) and diffuse optical spectroscopy (DOS) is developed, along with the basic elements of diffuse optical tomography (DOT). Diffuse correlation spectroscopy (DCS) is also discussed, which uses temporal correlation functions of diffusing light to measure blood flow. Essential instrumentation and representative results from brain and breast imaging are presented. The diffusion model is based on the radiation transport equation (RTE), which describes light propagation in tissues. The RTE is approximated using the $P_{N}$ method, with the $P_{1}$ approximation being particularly useful for nearly isotropic light. The diffusion model allows for the separation of scattering and absorption effects, enabling the measurement of tissue properties such as hemoglobin, water, and lipid concentrations. The model is validated in various biological tissues and has been used to measure blood flow, oxygen extraction rates, and other physiological parameters. The review outlines the theoretical background of diffuse optics, including the photon diffusion formalism, source types, and boundary conditions. It discusses the use of frequency-domain and time-domain solutions to the diffusion equation, as well as the application of Green's functions for solving the diffusion equation in various geometries. The review also covers the determination of tissue chromophore concentrations using spectroscopy, with a focus on the optimal selection of wavelengths for accurate measurements. The differential pathlength approach is introduced for measuring changes in chromophore concentrations and scattering properties. The review concludes with a discussion of diffuse correlation spectroscopy (DCS), which measures blood flow by analyzing the temporal correlation of diffusing light. DCS has been validated in various biological tissues and has shown promise for continuous non-invasive monitoring of physiological parameters. The review highlights the versatility of diffuse optics in a wide range of applications, including functional imaging and monitoring of tissue properties.