Brane worlds may provide insight into the cosmological constant problem because a large vacuum energy on the brane can curve the extra dimensions rather than the local 4D spacetime. Moreover, such models with supersymmetric large extra dimensions reveal a tantalizing numerology, in which the size of the two extra dimensions can lead not only to the electroweak hierarchy but also to the observed dark energy scale. I will review this proposal, its promises and problems, and then describe some of the novel physics that can arise in 6D brane worlds. The dynamical stability of models in 6D supergravity constrains the matter content of the theory, but surprisingly this can be relaxed with negative tension branes. Meanwhile, the Kaluza-Klein mass gap can remain finite even in the infinite volume limit.