Summary: The Galileons are a set of terms within four-dimensional effective field theories, obeying symmetries that can be derived from the dynamics of a (3 + 1)-dimensional flat brane embedded in a 5-dimensional Minkowski bulk. These theories have some intriguing properties, including freedom from ghosts and a non-renormalization theorem that hints at possible applications in both particle physics and cosmology. In this brief paper, we will summarize our attempts over the last year to extend the Galileon idea in two important ways. We will discuss the effective field theory construction arising from flat branes, of co-dimension greater than 1, embedded in a flat background – the multi-Galileons – and we will then describe symmetric covariant versions of the Galileons, more suitable for general cosmological applications. While all these Galileons can be thought of as interesting four-dimensional field theories in their own rights, the work described here may also make it easier to embed them into string theory, with its multiple extra dimensions and more general gravitational backgrounds.