For two convex bodies K, E of the n-dimensional euclidean space and a non-negative real number x, the volume of K+xE is a polynomial of degree n in x, whose coefficients are, up to a constant, important measures associated to both sets, the relative quermassintegrals. This polynomial is called the (relative) Steiner polynomial of K (with respect to E). If we consider the Steiner polynomial as a formal polynomial in a complex variable, we are interested in studying geometric properties of its roots: their location in the complex plane, size, relation with other geometric magnitudes (in- and circumradius) and characterization of (families of) convex bodies by mean of properties of the roots. In this talk I will show the known results on this topic, which had its starting point in a problem posed by Teissier in 1982, in the context of Algebraic Geometry.