In the early 1960s, Vinberg gave a description of homogeneous convex cones as cones of Hermitian positive de finite matrices in a matrix T-algebra $M_n$ of$ (n \times n)$-matrices whose diagonal entries are just real numbers, but off-diagonal elements belong to different vector spaces. It turns out that rank 3 special Vinberg cones (corresponding to Clifford algebras) have important applications to Supergravity. No special background is required. The talk is based on joint works with V. Cortes; and with A. Marrani and A. Spiro.n