Blazars are the most extreme class of active galactic nuclei (AGNs), also the largest source class of identifiied by Fermi extragalactic sky. Extensive data analyses of blazars has confirmed that the gamma-ray emission is an essential observational tool for understanding the physics of the central engines of AGNs. Their distribution of the spectral and other characteristics, and cosmological evolutions provide much more necessary information for constraining or the studies of the formation and growth of central black holes of galaxies. In this talk, I will use parametric and/or non-parametric methods to construct gamma-ray luminosity function (GLF) of Blazars, and study their cosmological evolution and discuss their contribution to the extragalactic gamma-ray background (EGB). The GLF and EGB also can be used to constrain the Hubble Constant and Matter Density of the Universe.

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