  High-energy logarithmic correction are enhanced when the ratio, $x =
\frac{Q^2}{s}$ between the typical energy scale of a scattering process $Q$ and
the total centre of mass energy available $s$ is small. We discuss recent
developments on their resummation in differential cross sections in rapidity,
transverse momentum and invariant mass and their application to heavy flavour
production at the LHC.
