I will survey some topics about hyperbolic polynomials and their determinantal representations, and hyperbolicity cones and representations thereof by linear matrix inequalities (spectrahedral cones). Time permitting I will then discuss two neighbouring topics: (a) a generalization of hyperbolicity from hypersurfaces to higher codimensional subvarieties, and a related class of determinantal representations (that yield linear determinantal representations of the Chow form); (b) complex multivariate polynomials that are stable (i.e., zero free) with respect to the unit polydisc, and determinantal representation that witness stability.