  The present experimental results on neutrino flavour oscillations provide
evidence for non-zero neutrino masses, but give no hint on their absolute mass
scale, which is the target of beta decay and neutrinoless double-beta decay
experiments. Crucial complementary information on neutrino masses can be
obtained from the analysis of data on cosmological observables, such as the
anisotropies of the cosmic microwave background or the distribution of
large-scale structure. In this review we describe in detail how free-streaming
massive neutrinos affect the evolution of cosmological perturbations. We
summarize the current bounds on the sum of neutrino masses that can be derived
from various combinations of cosmological data, including the most recent
analysis by the WMAP team. We also discuss how future cosmological experiments
are expected to be sensitive to neutrino masses well into the sub-eV range.
