Dennis The

Cartan and Engel gave the first geometric realisations of the (complex) exceptional simple Lie algebra $G_2$, namely as the symmetries of various differential geometric structures.  I'll describe generalizations of this story to the other exceptional simple Lie algebras, and more recently the exceptional simple Lie superalgebras $G(3)$ (joint work with Kruglikov and Santi) and $F(4)$ (joint work with Santi).