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The development and implementation of high-stability monochromators in state-of-the-art aberration-corrected scanning transmission electron microscopes has enabled materials characterization with an energy resolution as good as 3 meV. This allows the vibrational modes, which would otherwise be obscured by the energy spread of the electron beam, to be probed with very high precision in molecular materials. Since the vibrational energies depend on the weight of the atomic nuclei, vibrational spectroscopy can distinguish isotopes whose only difference lies in their neutron content. This opens up isotopic analysis and mapping in transmission electron microscopy as two important new research areas. Here, we review the monochromated electron energy loss spectroscopy (EELS) instrumentation, discuss optimal methods for probing beam-sensitive materials without destroying them, and review key nanoscale isotope-resolved results.