  We review the systematics of Mandelstam cut contributions to planar
scattering amplitudes in the multi-Regge limit. Isolating the relevant cut
terms, we explain how the BFKL expansion can be used to construct the
perturbative n-point multi-Regge limit amplitude in certain kinematic regions
from a finite number of basic building blocks. At three loops and at leading
logarithmic order, two building blocks are required. Their symbols are
extracted from the known three-loop six-point and seven-point symbols for
general kinematics. The new seven-point building block is constructed in terms
of single-valued multiple polylogarithms to the extent it can be determined
using the symbol as well as further symmetry and consistency constraints.
Beyond the leading logarithmic order, the subleading and sub-subleading terms
require two and one further building block, respectively. The latter could
either be reconstructed from further perturbative data, or from BFKL integrals
involving yet-unknown corrections to the central emission block.
