Heritable thoracic aortic disease (HTAD) is a term used to define a large group of disorders characterized by the occurrence of aortic events, mainly represented by aneurysm or dissection. These events generally involve the ascending aorta, although the involvement of other districts of the aorta or peripheral vessels may occur. HTAD can be classified as non-syndromic if the disorder is limited to the aorta, and syndromic when associated with extra-aortic features. About 20–25% of patients with non-syndromic HTAD exhibit a family history of aortic disease. Thus, a careful clinical evaluation of the proband and the first-degree family members is required to differentiate familial and sporadic cases. Genetic testing is essential since it allows confirmation of the etiological diagnosis of HTAD (particularly in patients with a significant family history) and may guide family screening. In addition, genetic diagnosis significantly impacts patients’ management since the different conditions significantly differ with respect to natural history and treatment strategies. The prognosis in all HTADs is determined by the progressive dilation of the aorta, potentially leading to acute aortic events, such as dissection or rupture. Moreover, the prognosis varies according to the underlying genetic mutations. This review aims to describe the clinical characteristics and natural history of the most common HTADs, with particular emphasis on the role of genetic testing in risk stratification and management.