Phase diagrams of some important theories like quantum chromodynamics (QCD), are only accessible through numerical simulations with only finite degrees of freedom. Information about critical phenomena can then only inferred through finite size scaling studies of various moments of the order parameter. Alternatively, one can study the complex zeros of the grand canonical partition function, known as Lee-Yang zeros, which are accessible as poles of the thermodynamic variables. Moreover the temperature and volume scaling of these poles can be used as a probe to understand the nature of phase transitions in many systems. We will discuss here the recent progress that has been made in this direction with respect to the Roberge-Weiss transition, the 2D Ising model and the conjectured QCD critical point. We will further discuss results on the universal location of Lee-Yang edge singularity from continuum extrapolated scaling function for some $O(N)$ models in $3-d$.