Superembeddings, Non-Linear Supersymmetry and 5-branes

We examine general properties of superembeddings, i.e., embeddings of supermanifolds into supermanifolds. The connection between an embedding procedure and the method of non-linearly realised supersymmetry is clarified, and we demonstrate how the latter arises as a special case of the former. As an illustration, the super-5-brane in 7 dimensions, containing a self-dual 3-form world-volume field strength, is formulated in both languages, and provides an example of a model where the embedding condition does not suffice to put the theory on-shell.