Peculiar velocities of galaxies are deviations from the Hubble flow. They are due to the gravitational interaction of galaxies gravitational potential with the underlying dark matter overdensity field. Thus, peculiar velocities of galaxies contain a lot of information about the LCDM model and particularly about the linear structure formation theory. Tracing the peculiar velocity field of galaxies can consequently constrain the location of dark matter, the expansion rate (via the Hubble constant) and the growth rate of structures, which in turns depends on the properties of dark energy.
Considering the CosmicFlows data, a catalog containing around 15,000 luminosity distance and redshift measurements, I will present how extragalactic measurements can be modeled to estimate the linear peculiar velocity field of the Local Universe up to redshift 0.05. I will also present how a full bayesian framework enables us to accurately account for prior information in order to reconstruct the most precise mapping of the cosmic structures of the Local Universe. Eventually, I will underline how such model can be improved so that peculiar velocity analyses can go from cosmography to Cosmology, and constrain the fundamental cosmological parameters.