Let Phi be a finite root system. A Phi-grading of a group G is
a family of subgroups of G satisfying certain axioms that
are inspired by the family of root subgroups in a Chevalley group.
In the 1990s Shi showed that the root subgroups of Phi-grading
are coordinatized by an associative ring if Phi is
simply laced, irreducible and of rank at least three.
For the remaining types there are only partial results available.
In my talk I will present some recent results about
Phi-gradings of groups which are motivated by the theory
of buildings and applications to rank one groups
of exceptional type. This is joint work with Richard Weiss.