Higgs Physics at future Linear Colliders - A Case for precise Vertexing

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.