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We derive a complete geometrical characterisation of a large class of$AdS_3$, $AdS_4$ and $AdS_5$ supersymmetric spacetimes in eleven-dimensionalsupergravity using G-structures. These are obtained as special cases of a classof supersymmetric $\mathbb{R}^{1,1}$, $\mathbb{R}^{1,2}$ and $\mathbb{R}^{1,3}$geometries, naturally associated to M5-branes wrapping calibrated cycles inmanifolds with $G_2$, SU(3) or SU(2) holonomy. Specifically, the latter classis defined by requiring that the Killing spinors satisfy the same set ofprojection conditions as for wrapped probe branes, and that there is noelectric flux. We show how the R-symmetries of the dual field theories appearas isometries of the general AdS geometries. We also show how known solutionspreviously constructed in gauged supergravity satisfy our more generalG-structure conditions, demonstrate that our conditions for half-BPS $AdS_5$geometries are precisely those of Lin, Lunin and Maldacena, and construct somenew singular solutions.Comment: 1+56 pages, LaTeX; v2, references added; v3, minor corrections, final  version to appear in JHE

AdS spacetimes from wrapped M5 branes