A new insight into oxidative stress is based on oxidative deoxyribonucleic acid (DNA) damage. DNA is the pivotal biopolymer for life and health. Arterial hypertension (HT) is a globally common disease and a major risk factor for numerous cardiovascular (CV) conditions and non-cardiac complications, making it a significant health and socio-economic problem. The aetiology of HT is multifactorial. Oxidative stress is the main driver. Oxidative DNA damage (oxidised guanosine (8OHdG), strand breaks (SSBs, DSBs)) seems to be the crucial and initiating causal molecular mechanism leading to HT, acting through oxidative stress and the resulting consequences (inflammation, fibrosis, vascular remodelling, stiffness, thickness, and endothelial dysfunction). In light of the current European Society of Cardiology (ESC) guidelines with defined gaps in the evidence, this manuscript, for the first time, (1) summarizes evidence for oxidative DNA damage in HT and other CV risk factors, (2) incorporates them into the context of known mechanisms in HT genesis, (3) proposes the existing concept of HT genesis innovatively supplemented with oxidative DNA damage, and (4) mentions consequences such as promising new targets for the treatment of HT (DNA damage response (DDR) pathways).