  A valuable amount of information is available in peculiar velocities of
galaxies. Peculiar velocity surveys have recently allowed the discovery of
potential problems with LCDM. Nonetheless, their direct observation through
distance measurements remains a daunting task. Another way of considering the
problem is to use orbit reconstruction methods assuming some mass-to-light
assignment for galaxies. We give here two applications of this procedure for
the study of large-scale bulk flows and the dynamics of voids in the Local
Universe. We concentrate our study on the use of the Monge-Ampere-Kantorovitch
reconstruction technique. Using peculiar velocities reconstructed from the
2MASS Galaxy Redshift Survey, and after comparison with the NGB-3k peculiar
velocity catalog, we look in the details of these peculiar velocities. More
particularly, we estimate the constraints that the peculiar velocities put on
the cosmology. The information on dynamics that is included in reconstructed
orbits of galaxies also allows us to have a much better prescription for
defining and identifying voids in simulations and redshift catalogs. We present
this new technique and how voids may give us additional constraints on
cosmology with current and future surveys.
