Duality in projective geometry is a well-known phenomenon in any dimension. On the other hand, geometric triality deals with points and spaces of two different kinds in a seven-dimensional projective space. It goes back to Study (1913) and Cartan (1925), and was soon realizedthat this phenomenon is tightly related to the algebra of octonions, and the order 3 outer automor-phisms of the spin group in dimension 8.Tits observed, in 1959, the existence of two different types of geometric triality. One of themis related to the octonions, but the other one is better explained in terms of a class of nonunitalcomposition algebras discovered by the physicist Okubo (1978) inside 3x3-matrices, and which hasled to the definition of the so called symmetric composition algebras. This talk will review the history, classification, and their connections with the phenomenon oftriality, of the symmetric composition algebras.