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We introduce the class of outerspatial 2-complexes as the naturalgeneralisation of the class of outerplanar graphs to three dimensions.Answering a question of O-joung Kwon, we prove that a locally 2-connected2-complex is outerspatial if and only if it does not contain a surface ofpositive genus as a subcomplex and does not have a space minor that is ageneralised cone over $K_4$ or $K_{2,3}$.  This is applied to nested plane embeddings of graphs; that is, planeembeddings constrained by conditions placed on a set of cycles of the graph.

Outerspatial 2-complexes: Extending the class of outerplanar graphs to three dimensions