The large scale structure of the universe are in motions, which are generated from the primordial gravitational perturbations, themselves amplified by gravitational instabilities. These motions, observable through the emission spectrum of objects such as galaxies in the sky, are called cosmic flows once averaged on sufficiently large scales. The study of cosmic flows is important as it is the main probe for the growth of structures at low redshift (z < 0.1) and it also impacts the determination of the Hubble parameter H0. By being a lot more sensitive to large scales, cosmic flows also informs us directly on the distribution of matter beyond the limits of their original surveys.
We will review existing data (CF3, CF4, 2MTF, Pantheon,...) and advances in statistical analysis that is leading to regain interests in cosmic flows as a direct cosmological probe. Particularly, the new advances hinge on a better understanding of the limits and strengths of linear perturbation theory, and the inclusion of a more and more forward modeling aspects. We will investigate how these advances have lead to a more consistent pictures of our understanding of cosmology, but also to lingering tensions between observations of the CMB sky and the clustering at low redshift.