We present a data-driven approach to understand the star formation in dark matter halos over cosmic time. With a simple empirical model and advanced tools for Bayesian inference, we try to constrain how galaxies have assembled their stars across cosmic time using stellar mass functions (SMFs) and the luminosity function of cluster galaxies. The key ingredients of the empirical model include dark halo merger trees and a generic function that links star formation rate (SFR) to the host halos. We found a new characteristic redshift zc ~ 2 above which the SFR in low mass halos < 1011 solar mass must be enhanced relative to that at lower z. This leads to some interesting predictions, for instance, a signicant old stellar population in present-day dwarf galaxies with mass of 108 solar mass and steep low-mass end slopes of high redshift SMFs. The constrained empirical model can be combined with other other observational constraints to infer the physics behind the evolution of galaxies. The classical bulge mass could be derived from the major mergers of the host galaxies. Applying the central black hole (BHs) - classical bulge relation, it predicts all galaxies with stellar mass less than 1010.5 solar mass host intermediate mass BHs (MBH < 107solar mass). Using the gas phase metallicity we study the evolution of gas and metal content of star forming galaxies and the infow and outfow rates. About 60% of the metals produced have been lost. At low redshift (z < 1) the accretion of pristine gas should be lower by a factor of few than expected and the loading factor of gas outfow that is not recycled is of order of unity. The empirical model also serves as basis to study the evolution of satellite galaxies. The progenitors of present-day satellites can be initialized using this empirical model. The physically motivated models of quenching of star formation in satellites, including strangulation, ram pressure stripping of cold gas disks, and tidally triggered starburst, are tested against statistics of the group catalogs.