Primary hyperparathyroidism, a disorder in which there is a tendency for hypercalcaemia caused by autonomous overproduction of parathyroid hormone, is common, especially in postmenopausal women. Although parathyroidectomy is indicated for symptomatic patients, most individuals with the disorder are asymptomatic and without classic complications, such as renal stones and osteoporosis, at diagnosis. Consensus guidelines suggest which individuals might be suitable for medical follow-up rather than parathyroidectomy, but there are no long-term randomised controlled trials to support the safety of medical surveillance, and some patients progress with time. Data from observational studies suggest that cardiovascular morbidity and mortality are increased in patients with primary hyperparathyroidism, and might be predicted by parathyroid hormone concentrations, even in individuals with asymptomatic primary hyperparathyroidism. Whether parathyroidectomy improves cardiovascular outcomes in patients with asymptomatic primary hyperparathyroidism is unproven, but data suggest that surgery decreases fracture risk and might improve neuropsychological symptoms. Studies also show that patients with normocalcaemic (subclinical) hyperparathyroidism and hypoparathyroidism have a low risk of progression to overt disease, but their long-term risks are not defined. In this Review, we explore the increasing range of asymptomatic parathyroid disorders, focusing on current evidence about their natural history and potential complications, with a particular emphasis on primary hyperparathyroidism.