This presentation discusses numerical studies of Yang-Lee edge singularities in 2D spin models. The studies use the finite-size scaling behavior of quantum spin chains to obtain information on the Yang-Lee edge singularities of discrete spin models. The studies provide values for Fisher's sigma exponent and candidate conformal field theories. For the 2D Ising model, known results are reviewed. For the 2D 3-state Potts model, new results are presented.