Jellyfish represent one of the earliest and simplest examples of swimming by a macroscopic organism. Through a process of elastic deformation and recoil, jellyfish propulsion is generated via the coordinated contraction of its elastic bell by its coronal swimming muscles and a complementary re-expansion that is passively driven by stored elastic energy. In this talk, we will begin by first examining the role of mechanical resonance in producing faster or more efficient locomotion. We will then shift our focus onto how the underlying acephalic neuromuscular organization of their bell allows for complicated swimming behaviors, such as steering and maneuvering. Using an immersed boundary framework validated with flow visualization studies, we will examine the mechanics of swimming by incorporating material models that are informed by the musculature present in jellyfish into a model of the elastic jellyfish bell in three dimensions. Preliminary work regarding optimal group behavior of benthic upside-down jellyfish will also be discussed.