  Serre in "Trees" laid down the fundamentals of the theory of groups acting on
simplicial trees. In particular, Bass-Serre theory makes it possible to extract
information about the structure of a group from its action on a simplicial
tree. Serre's original motivation was to understand the structure of certain
algebraic groups whose Bruhat--Tits buildings are trees. In this survey we will
discuss the following generalizations of ideas from "Trees": the theory of
isometric group actions on $\Lambda$-trees and the theory of lattices in the
product of trees where we describe in more detail results on arithmetic groups
acting on a product of trees.
