I will start with a basic introduction to planar algebras. I will then discuss recent joint work with Scott Morrison (arXiv:1208.3637) and recent joint work with Stephen Bigelow (arXiv:1208:1564). With Morrison, we construct a new exotic subfactor planar algebra using Bigelow's jellyfish algorithm. With Bigelow, we determine exactly when a planar algebra has a presentation by generators and jellyfish relations.