Many of the most exotic neutron-proton asymmetric nuclei are produced in relatively small numbers in high-energy fragmentation reactions. They are produced as fast secondary beams with energies of 100 MeV per nucleon or more. Developments made and recent results that both exploit and assess fast one-and two-nucleon removal reactions from such secondary beams are reviewed. This includes very recent work that interfaces the sudden, eikonal reaction models used with more ab-initio nuclear

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... inputs. The potential use of neutron pick-up reactions to study particle-like states in exotic nuclei is also outlined.