  We analyse generic AdS flux backgrounds preserving eight supercharges in
$D=4$ and $D=5$ dimensions using exceptional generalised geometry. We show that
they are described by a pair of globally defined, generalised structures,
identical to those that appear for flat flux backgrounds but with different
integrability conditions. We give a number of explicit examples of such
"exceptional Sasaki-Einstein" backgrounds in type IIB supergravity and
M-theory. In particular, we give the complete analysis of the generic AdS$_5$
M-theory backgrounds. We also briefly discuss the structure of the moduli space
of solutions. In all cases, one structure defines a "generalised Reeb vector"
that generates a Killing symmetry of the background corresponding to the
R-symmetry of the dual field theory, and in addition encodes the generic
contact structures that appear in the $D=4$ M-theory and $D=5$ type IIB cases.
Finally, we investigate the relation between generalised structures and
quantities in the dual field theory, showing that the central charge and
R-charge of BPS wrapped-brane states are both encoded by the generalised Reeb
vector, as well as discussing how volume minimisation (the dual of $a$- and
$\mathcal{F}$-maximisation) is encoded.
