  This is a survey of the recent development of the study of topological full
groups of etale groupoids on the Cantor set. Etale groupoids arise from
dynamical systems, e.g. actions of countable discrete groups, equivalence
relations. Minimal Z-actions, minimal Z^N-actions and one-sided shifts of
finite type are basic examples. We are interested in algebraic, geometric and
analytic properties of topological full groups. More concretely, we discuss
simplicity of commutator subgroups, abelianization, finite generation,
cohomological finiteness properties, amenability, the Haagerup property, and so
on. Homology groups of etale groupoids, groupoid C*-algebras and their K-groups
are also investigated.
