After introducing the Taylor expansion method for lattice QCD calculations at non-vanishing baryon chemical potential, I will scrutinize the limitations of the method arising from the presence of Yang-Lee edge singularities in the QCD phase diagram. I will discuss a newly introduced resummation scheme for the Taylor expansion to overcome this limitation and show the efficacy of this scheme using a simple solvable model. I will present some results from realistic lattice QCD calculations utilizing this resummation scheme. I will conclude by introducing a generalized version of the scheme that can resum the recently proposed multi-parameter Taylor expansion.