This is a comprehensive discussion of automatic continuity issues in the contexts mentioned. Emphasizing homomorphisms and derivations, and always relating the not necessarily associative issues to their associative analogues, this account lists 26 open questions. A list of the section headers gives a good impression of the contents: Nonassociative Banach algebras, radicals, homomorphisms, continuity under conditions on the range, in the associative case, and in the nonassociative case, continuity under conditions on the domain, derivations, continuity in the associative context, and in the nonassociative, the Singer-Wermer conjecture in the associative context, and in the nonassociative.