Reverse mathematics is a research program on foundations of mathematics, whose aim is to isolate axioms or assumptions needed to prove a theorem of ordinary mathematics. Among others, weak Koenig's lemma, which asserts that every infinite binary tree has an infinite path, is a crucial assumption often used to prove theorems that rely on some form of compactness, such as the maximum principle or Goedel's completeness theorem. In this talk, we overview basic results and recent improvements on models of weak Koenig's lemma.