Improving our understanding of rare disease and developing new therapies can only succeed through global collaboration. Whole genome sequencing is increasingly being deployed to diagnose rare disease, and can be combined with machine-learning tools that analyze patient photos to identify phenotypes. Clinical interpretation of genomes and phenotypic data in rare disease depends on sharing individual patient data internationally. Data sharing is essential in rare disease contexts, to support the diagnosis of patients, recruitment into trials, the development of precision diagnostics and therapies, and clinical trial transparency. The sharing of rich molecular and phenotypic data presents privacy risks for rare disease patients, though many want to see their data made available to improve their care and advance research. Informed consent, access governance, and access technologies are important to realize the benefits of data sharing while mitigating risks. Rare disease patients should be involved in the design of data sharing governance to ensure it responds to their particular needs and preferences.