  This paper considers the spacetimes describing pp-waves propagating on
extremal non-dilatonic branes. It is shown that an observer moving along a
geodesic will experience infinite curvature at the horizon of the brane, which
should therefore be regarded as singular. Taking the decoupling limit of these
brane-wave spacetimes gives a pp-wave in AdS, the simplest example being the
Kaigorodov spacetime. It has been conjectured that gravity in this spacetime is
dual to a CFT in the infinite momentum frame with constant momentum density. If
correct, this implies that the CFT must resolve the singularity of the bulk
spacetime. Evidence in favour of this conjecture is presented. The unbroken
conformal symmetries determine the scalar 2-point function up to an arbitrary
function of one variable. However, an AdS/CFT calculation shows that this
function is constant (to leading order in $1/N^2$) and the result is therefore
the same as when the full conformal symmetry is unbroken. This paper also
discusses a recently discovered Virasoro symmetry of metrics describing
pp-waves in AdS and naked singularities in the Randall-Sundrum scenario.
