  The focusing theorem in General Relativity underlies causality, singularity
theorems, entropy inequalities, and more. In AdS/CFT, we show that focusing in
the bulk leads to a bound on CFT $n$-point functions that is generally stronger
than causality. Causality is related to the averaged null energy condition
(ANEC) on the boundary, while focusing is related to the ANEC in the bulk. The
bound is derived by translating the Einstein equations into a relation between
bulk and boundary light-ray operators. We also discuss the consequences of
focusing for the flat space $S$-matrix, which satisfies a similar inequality,
and give a new derivation of bounds on higher derivative operators in effective
field theories. The string theory $S$-matrix and CFT correlators in conformal
Regge theory also satisfy the focusing bound, even though in these cases it
cannot be derived from the standard focusing theorem.
