Constraining the density dependence of symmetry energy has been a major focus in recent times both in the context of finite nuclei as well as astrophysical objects e.g. neutron stars to understand the basic nature of nuclear force. In this talk, I will be dealing with mean field models both relativistic as well as non-relativistic in nature. In the first part of the talk, I will try to demonstrate how binding energy of some highly asymmetric nuclei (which were never part of the fit to obtain the parameters of a relativistic mean field model) helps to constrain the density dependence of symmetry energy. To do that some aspects of covariance analysis (which tells about how good or bad your model is) will be discussed. In the second part, I will try to demonstrate some ambiguities in the slope parameter (which tells about density dependence) of symmetry energy using some well established set of mean field models. To circumvent this discrepancies I will demonstrate some aspects of macroscopic Droplet Model for nuclei and show that reason behind these ambiguities can be understood. On the basis of the results I demonstrate, I will try to give some conclusions.