  We derive a geometrical characterisation of a large class of AdS_3 and AdS_2
supersymmetric spacetimes in IIB supergravity with non-vanishing five-form flux
using G-structures. These are obtained as special cases of a class of
supersymmetric spacetimes with an $\mathbb{R}^{1,1}$ or $\mathbb{R}$ (time)
factor that are associated with D3-branes wrapping calibrated 2- or 3- cycles,
respectively, in manifolds with SU(2), SU(3), SU(4) and G_2 holonomy. We show
how two explicit AdS solutions, previously constructed in gauged supergravity,
satisfy our more general G-structure conditions. For each explicit solution we
also derive a special holonomy metric which, although singular, has an
appropriate calibrated cycle. After analytic continuation, some of the classes
of AdS spacetimes give rise to known classes of BPS bubble solutions with
$\mathbb{R}\times SO(4)\times SO(4)$, $\mathbb{R}\times SO(4)\times U(1)$, and
$\mathbb{R}\times SO(4)$ symmetry. These have 1/2, 1/4 and 1/8 supersymmetry,
respectively. We present a new class of 1/8 BPS geometries with
$\mathbb{R}\times SU(2)$ symmetry, obtained by analytic continuation of the
class of AdS spacetimes associated with D3-branes wrapped on associative
three-cycles.
