This narrative review summarizes data on classical and nonclassical manifestations of primary hyperparathyroidism (PHPT). It is based on a rigorous literature search, inclusive of a Medline search for systematic reviews from 1940 to December 2020, coupled with a targeted search for original publications, covering four databases, from January 2013–December 2020, and relevant articles from authors’ libraries. We present the most recent information, identify knowledge gaps, and suggest a research agenda. The shift in the presentation of PHPT from a predominantly symptomatic to an asymptomatic disease, with its varied manifestations, has presented several challenges. Subclinical nephrolithiasis and vertebral fractures are common in patients with asymptomatic disease. The natural history of asymptomatic PHPT with no end organ damage at diagnosis is unclear. Some observational and cross-sectional studies continue to show associations between PHPT and cardiovascular and neuropsychological abnormalities, among the different disease phenotypes. Their causal relationship is uncertain. Limited new data are available on the natural history of skeletal, renal, cardiovascular, neuropsychological, and neuromuscular manifestations and quality of life. Normocalcemic PHPT (NPHPT) is often diagnosed without the fulfillment of rigorous criteria. Randomized clinical trials have not demonstrated a consistent long-term benefit of parathyroidectomy (PTX) versus observation on nonclassical manifestations. We propose further refining the definition of asymptomatic disease, into two phenotypes:​ one without and one with evidence of target organ involvement, upon the standard evaluation detailed in our recommendations. Each of these phenotypes can present with or without non-classical manifestations. We propose multiple albumin-adjusted serum calcium determinations (albumin-adjusted and ionized) and exclusion of all secondary causes of high parathyroid hormone (PTH) when establishing the diagnosis of NPHPT. Refining the definition of asymptomatic disease into the phenotypes proposed will afford insights into their natural history and response to interventions. This would also pave the way for the development of evidence-based guidance and recommendations.