Abstract: Physical laws are generally expressed as mathematical relations between different physical quantities. The validity of these relations lies in their consistency with experimental results which is achieved by introducing some fundamental constants. To retain the universality of physical laws these constants are supposed to be independent of the time and location of the experiment. The focus of the discussion would be about the constancy of some of these fundamental constants on cosmological scales. Further, the talk will cover my recent attempts to probe a few such constants like mass of graviton and the Fermi coupling constant using most recent cosmological observations.