Partial groups are structures with partially-defined n-ary multiplications. They were introduced by Chermak in his proof of the existence and uniqueness of centric linking systems for saturated fusion systems, a major recent result in p-local finite group theory. We'll introduce these gadgets from the perspective of symmetric simplicial sets and give some examples. We'll also discuss a way to think about (partial) actions of partial groups, inspired by the classical notion of a star injective functor between groupoids. Especially interesting are the "characteristic" actions, which control which multiplications are valid in the partial group. These are a key ingredient in computational tools for determining when a given partial group is a d-Segal space in the sense of Dyckerhoff and Kapranov. Based on joint work with Justin Lynd.