Understanding the formation of stars, galaxies and black holes in primordial cosmological epochs is one of the most striking challenges of modern astrophysics. In order to do that, theoretical models are embedded in large numerical simulations that follow the behavior of cosmic gas in different environments, its cooling capabilities, star formation processes and feedback effects. During the talk, results from this kind of studies will be presented to shed light on the formation epoch of the very first objects and their impacts on subsequent structure evolution. The transition from a primordial dark Universe, with pristine H and He chemical composition, to the present-day ‘bright’ Universe, enriched with heavy elements and molecules, will be discussed as well as the role of different model assumptions on the solidity of the results. Finally, theoretical predictions will be compared against a number of observables (e.g. luminosity functions, star formation rates, metallicities, abundance ratios) to draw conclusions on our comprehension of cosmic history and the expectations from future instruments, such as JWST, Roman/WFIRST, ELT.