Constructing Galileons

In this plenary talk delivered at the DISCRETE 2014 conference in London, I briefly summarize the ideas behind and attractive properties of the Galileon field theories, and describe a broad class of scalar field theories that share these properties. After describing how Galileons arise, and commenting on their fascinating properties, in the latter half of the talk I focus on novel ways of constructing Galileon-like theories, using both the probe brane construction, and the coset construction.