A total of 1 out of 10 patients with primary hyperparathyroidism (PHP) presents an underlying genetic form, such as multiple endocrine neoplasia types 1, 2A, etc., as well as hyperparathyroidism–jaw tumour syndrome (HJT). We aimed to summarise the recent data, thus raising more awareness regarding HJT, from the clinical perspective of PHP in association with the challenges and pitfalls of CDC73 genetic testing and parafibromin staining. This narrative review included a sample-focused analysis from the past decade according to a PubMed search. We identified 17 original human studies (≥4 patients per article). The mean age at disease onset was between 20.8 and 39.5 years, while the largest study found that 71% of patients had HJT recognised before the age of 30. Males and females seemed to be equally affected, in contrast with sporadic PHP. PHP represented the central manifestation of HJT, occurring as the first manifestation in up to 85% of HJT cases. A biochemistry panel found a mean serum calcium level above the level of 12 mg/dL in PHP. PTH was elevated in HJT as well, with average values of at least 236.6 pg/mL. The most frequent pathological type in PHP was a parathyroid adenoma, but the incidence of a parathyroid carcinoma was much higher than in non-HJT cases (15% of all parathyroid tumours), with the diagnosis being established between the age of 15 and 37.5. In some families up to 85% of carriers suffered from a parathyroid carcinoma thus indicating that certain CDC73 pathogenic variants may harbour a higher risk. An important issue in HJT was represented by the parafibromin profile in the parathyroid tumours since in HJT both parathyroid adenomas and carcinomas might display a deficient immunoreactivity. Another frequent manifestation in HJT was ossifying fibromas of the jaw (affecting 5.4% to 50% of patients; the largest study found a prevalence of 15.4%). HJT was associated with a wide variety of kidney lesion (mostly: kidney cysts, with a prevalence of up to 75%, and renal tumours involved in 19% of patients). The risk of uterine lesions seemed increased in HJT, especially with concern to leiomyomas, adenofibromas, and adenomyosis. The underlying pathogenic mechanisms and the involvement of CDC73 pathogenic variants and parafibromin expression are yet to be explored. Currently, the heterogeneous expression of parafibromin status and, the wide spectrum of CDC73 mutations including the variety of clinical presentations in HJT, make it difficult to predict the phenotype based on the genotype. The central role of HJT-PHP is, however, the main clinical element, while the elevated risk of parathyroid carcinoma requires a special awareness.