Measurements of the helium-cluster breakup and neutron removal cross-sections for neutron-rich Be isotopes 10–12,14Be are presented. These have been studied in the 30 to 42 MeV/nucleon energy range where reaction measurements are proposed to be sensitive to the cluster content of the ground-state wave-function. These measurements provide a comprehensive survey of the decay processes of the Be isotopes by which the valence neutrons are removed revealing the underlying α–α core-cluster structure. The measurements indicate that clustering in the Be isotopes remains important up to the drip-line nucleus 14Be and that the dominant helium-cluster structure in the neutron-rich Be isotopes corresponds to α–Xn–α.