  This article discusses some recent trends in Ramsey theory on infinite
structures. Trees and their Ramsey theory have been vital to these
investigations. The main ideas behind the author's recent method of trees with
coding nodes are presented, showing how they can be useful both for coding
structures with forbidden configurations as well as those with none. Using
forcing as a tool for finite searches has allowed the development of Ramsey
theory on such trees, leading to solutions for finite big Ramsey degrees of
Henson graphs as well as infinite dimensional Ramsey theory of copies of the
Rado graph. Possible future directions for applications of these methods are
discussed.
