By combining our two major theories, that of the very large, General Relativity, and that of the very small, Quantum Physics (in particular nuclear and particle physics), it has been possible to construct a relatively accurate description of the life and death of stars.
The majority of stars evolve in a equilibrium between fusion processes, forming higher and higher atomic elements until Iron, and the ever contracting force of gravity.
The end process and product of the evolution depends on the overall mass of the stars, producing white dwarfs, neutron stars or black holes. Actually the final nature of all of these objects represents another crucial challenge to our current understanding of cosmic phenomena.