Ya.B.Zeldovich (1914-1987) contribution to cosmology is well-known: Harrison-Zeldovich spectrum, his approximation for the growth of primordial perturbation, Sunyaev-Zeldovich effect, etc. Here I point out some less known, but very important results of Zeldovich. Based on my personal communication with him, I will tell what was his most favourite problem in physics to which he would return throughout his life. What is the Zeldovich number. What is his "gradient mechanism of transition to detonation". How could he find the non-linear stabilization of Landau-Darrieus instability. Those results are important for flames and explosions of supernovae, for ionization-recombination fronts in cosmology and for turbulence in stars and clusters of galaxies. In regard to this I will briefly describe our current research of supernova hydrodynamics. Among other things, I will explain wonderful results by Zeldovich on non-linear instability of any star to a collapse into black hole and on "How quantum mechanics helps us to understand classical mechanics"