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The "polyhedral product functor" produces a space from a simplicial complex Land a collection of pairs of spaces, {(A(i),B(i))}, where i ranges over thevertex set of L. We give necessary and sufficient conditions for the resultingspace to be aspherical. There are two similar constructions, each of whichstarts with a space X and a collection of subspaces, {X_i} and then produces anew space. We give conditions for the results of these constructions to beaspherical. All three techniques can be used to produce examples of closedaspherical manifolds.  Abstract for Corrigenda: This note concerns two refinements to the earlierwork by the first author. First, when L is infinite, the definition ofpolyhedral product needs clarification. Second, the earlier paper omitted somesubtle parts of the necessary and sufficient conditions for polyhedral productsto be aspherical. Correct versions of these necessary and sufficient conditionsare given in the present paper.

Right-angularity, flag complexes, asphericity. \ Criteria for asphericity: corrigenda for "Right-angularity, flag complexes, asphericity"