Lorentzian polynomials link continuous convex analysis and discrete convex analysis via tropical geometry. The class of Lorentzian polynomials contains homogeneous stable polynomials as well as volume polynomials of convex bodies and projective varieties. I will give several combinatorial applications. No specific background will be needed to enjoy the talk. Joint work with Petter Brändén (https://arxiv.org/abs/1902.03719).