Peculiar velocity measurements however rely on noisy extragalactic distances estimation, which can be provided by Type Ia Supernovae observations. Because peculiar velocities of galaxies are deviations from the Hubble expansion law, they have poor signal to noise ratio and are particularly sensible to systematic uncertainties such as calibration errors, selection effects and unknown covariances. During this presentation I will present how to measure peculiar velocities and how to  map the Universe with them. I will detail how the statistical methods I develop can handle extragalactic distance measurements and lead to a velocity field reconstruction of our Local Universe so as constraints on cosmology. I will then show how future SNeIa surveys, in particular the Zwicky Transient Facility and the Large Synoptic Sky Survey, will allow us to accurately test General Relativity.