One of the key challenges for the next 10 years is to understand the first sources of light, the first stars and possibly accreting black holes. Their formation ended the cosmic dark ages at redshifts z ≃ 20 − 30, and signaled the transition from the simple initial state of the universe to one of ever increasing complexity. We here review recent progress in understanding the formation process of the first stars with numerical simulations, starting with cosmological initial conditions and modelling the detailed physics of accretion. Once formed, the first stars exerted crucial feedback on the primordial intergalactic medium, due to their input of radiation and of heavy chemical elements in the wake of supernova explosions. The current theoretical model posits that the first stars were predominantly very massive, typically ~100 M⊙. Our predictions will be tested with upcoming near-infrared observatories, such as the James Webb Space Telecope, in the decade ahead.