This review discusses the role of massive neutrinos in cosmology, focusing on how they affect cosmological perturbations and the current bounds on neutrino masses derived from various cosmological data. The authors highlight that while neutrino oscillation experiments provide evidence for non-zero neutrino masses, they do not determine their absolute scale. Cosmological observables, such as the cosmic microwave background (CMB) anisotropies and large-scale structure, offer crucial complementary information. The review covers the impact of free-streaming massive neutrinos on cosmological perturbations, including the evolution of power spectra and the background universe. It also summarizes the current bounds on neutrino masses from different cosmological data sets, including recent results from the Wilkinson Microwave Anisotropy Probe (WMAP) and galaxy redshift surveys. The authors discuss the prospects for future cosmological experiments to measure neutrino masses down to the sub-eV range and provide a comprehensive overview of the theoretical framework and observational constraints.This review discusses the role of massive neutrinos in cosmology, focusing on how they affect cosmological perturbations and the current bounds on neutrino masses derived from various cosmological data. The authors highlight that while neutrino oscillation experiments provide evidence for non-zero neutrino masses, they do not determine their absolute scale. Cosmological observables, such as the cosmic microwave background (CMB) anisotropies and large-scale structure, offer crucial complementary information. The review covers the impact of free-streaming massive neutrinos on cosmological perturbations, including the evolution of power spectra and the background universe. It also summarizes the current bounds on neutrino masses from different cosmological data sets, including recent results from the Wilkinson Microwave Anisotropy Probe (WMAP) and galaxy redshift surveys. The authors discuss the prospects for future cosmological experiments to measure neutrino masses down to the sub-eV range and provide a comprehensive overview of the theoretical framework and observational constraints.