I will review some (actually quite old) results by C. Borgs, J.T. Chayes, R. Kotecky and myself concerning the partition function zeros of the Ising model. The focus will be on the fact that, for specific boundary conditions, the zeros lie (in a suitable representation) on the unit circle. I will explain (1) the classic proof of the Lee-Yang circle theorem and (2) how one can nail the positions of the zeros up to exponentially small errors in the system size for the periodic boundary conditions. I may find time to explain how one uses this result to prove the so called Griffiths singularities in site-diluted Ising model.