We will discuss the singular structure of the QCD phase diagram, present in the vicinity of the Roberge-Weiss and chiral phase transitions in QCD. We discuss two methods to extract complex singularities from lattice QCD observables calculated at imaginary baryon chemical potential, rational approximations and Fourier coefficients. We emphasize that the singularities in the complex chemical potential plane can be interpreted in terms of Lee-Yang edge singularities with known universal scaling behavior. Their universal scaling manifests as properties of the order parameter scaling function 𝑓𝐺 . A particular parametrization of 𝑓𝐺 based on Schofield is frequently used, is presented. We show that the parametrization also exhibits the universal position of the Lee-Yang edge. We emphasize that scaling fits to the Lee-Yang edge can be used to determine the (non-universal) location of phase transitions in QCD.