From Spitzer mid infrared observations and measurements of peculiar velocities to constrained simulations of the local universe Galaxies are observational probes to study the Large Scale Structure. Their gravitational motions are tracers of the total matter density and therefore of the Large Scale Structure. Besides studies of structure formation and galaxy evolution rely on numerical cosmological simulations. Still only one universe observable from a given position in time and space is available for comparisons with simulations. The related cosmic variance affects our ability to interpret the results. Simulations constrained by observational data are a perfect remedy to this problem. Achieving such simulations requires the projects Cosmic flows and CLUES. Cosmic flows builds catalogs of accurate distance measurements to map deviations from the expansion. These measures are mainly obtained with the galaxy luminosity rotation rate correlation. We present the calibration of that relation in the mid infrared with observational data from Spitzer Space Telescope. Resulting accurate distance estimates will be included in the third catalog of the project. In the meantime two catalogs up to 30 and 150 Mpc h have been released. We report improvements and applications of the CLUES method on these two catalogs. The technique is based on the constrained realization algorithm. The cosmic displacement field is computed with the Zeldovich approximation. This latter is then reversed to relocate reconstructed three dimensional constraints to their precursors positions in the initial field. The size of the second catalog (8000 galaxies within 150 Mpc h) highlighted the importance of minimizing the observational biases. By carrying out tests on mock catalogs built from cosmological simulations a method to minimize observational bias can be derived. Finally for the first time cosmological simulations are constrained solely by peculiar velocities. The process is successful as resulting simulations resemble the Local Universe. The major attractors and voids are simulated at positions approaching observational positions by a few megaparsecs thus reaching the limit imposed by the linear theory.