The prevalence of obesity has tripled over the past five decades. Obesity, especially visceral obesity, is closely related to hypertension, increasing the risk of primary (essential) hypertension by 65–75%. Hypertension is a major risk factor for cardiovascular disease, the leading cause of death worldwide, and its prevalence is rapidly increasing following the pandemic rise in obesity. Although the causal relationship between obesity and high blood pressure (BP) is well established, the detailed mechanisms for such association are still under research. For more than thirty years sympathetic nervous system (SNS) and kidney sodium reabsorption activation, secondary to insulin resistance and compensatory hyperinsulinemia, have been considered as primary mediators of elevated BP in obesity. However, experimental and clinical data show that severe insulin resistance and hyperinsulinemia can occur in the absence of elevated BP, challenging the causal relationship between insulin resistance and hyperinsulinemia as the key factor linking obesity to hypertension. The purpose of Part 1 of this review is to summarize the available data on recently emerging mechanisms believed to contribute to obesity-related hypertension through increased sodium reabsorption and volume expansion, such as: physical compression of the kidney by perirenal/intrarenal fat and overactivation of the systemic/renal SNS and the renin-angiotensin-aldosterone system (RAAS). The role of hyperleptinemia, impaired chemoreceptor and baroreceptor reflexes, and increased perivascular fat is also discussed. Specifically targeting these mechanisms may pave the way for a new therapeutic intervention in the treatment of obesity-related hypertension in the context of ‘precision medicine’ principles, which will be discussed in Part 2.