We will review some recent advances in Ramsey Theory for trees focusing, in particular, on the Halpern-Lauchli Theorem. The Halpern-Lauchli Theorem (discovered in 1966) is a deep pigeon-hole principle for trees. It concerns partitions of the level product of a finite sequence of finitely branching trees. It has been the main tool for the development of Ramsey Theory for trees, a rich area of Combinatorics with important applications in Functional Analysis and Topology. A density version of the Halpern-Lauchli Theorem was conjectured from the late 1960s. This has been recently settled in the affirmative by Vassilis Kanellopoulos, Nikos Karagiannis and the speaker. We will discuss aspects of the proof as well as results pointing towards understanding some quantitative invariants related to the density Halpern-Lauchli Theorem