The concept of multidegrees provides the right generalization of the degree of a projective variety to a multiprojective setting. The study of multidegrees goes back to seminal work by van der Waerden in 1929. We will slowly introduce the notion of multidegrees of a multiprojective variety. A complete characterization of the positivity of multidegrees will be presented. Finally, we will apply our methods on multidegrees to settle a conjecture of Monical, Tokcan, and Yong for double Schubert polynomials and a particular case of a conjecture of the same authors for Grothendieck polynomials. We will report on joint works with Federico Castillo, Binglin Li, Fatemeh Mohammadi, Jonathan Montaño, and Naizhen Zhang.