  The discovery of a Higgs boson by the experiments at the LHC marks a major
breakthrough in particle physics, with far-reaching consequences for our
understanding of the fundamental principles of our Universe. To fully explore
this unique particle, experiments at high-energy electron-positron colliders
are being planned, providing substantial added benefit over the capabilities of
the LHC alone, such as model-independent measurements of couplings, constraints
on invisible decays and precise measurements of the self-coupling. This
contribution summarizes the Higgs physics program at such future facilities,
highlighting in particular also the role of precise vertexing in achieving the
ambitious goals of these experiments.
