Salt sensitivity, which is an increase in blood pressure in response to high dietary salt intake, is an independent risk factor for cardiovascular disease and mortality. It is associated with physiological, environmental, demographic, and genetic factors. This review focuses on the physiological mechanisms of salt sensitivity in populations at particular risk, along with the associated dietary factors. The interplay of mechanisms such as the renin–angiotensin aldosterone system, endothelial dysfunction, ion transport, and estrogen decrease in women contributes to development of salt sensitivity. Because of their effects on these mechanisms, higher dietary intakes of potassium, calcium, vitamin D, antioxidant vitamins, and proteins rich in L-arginine, as well as adherence to dietary patterns similar to the DASH (Dietary Approaches to Stop Hypertension) diet, can be beneficial to salt-sensitive populations. In contrast, diets similar to the typical Western diet, which is rich in saturated fats, sucrose, and fructose, together with excessive alcohol consumption, may exacerbate salt-sensitive changes in blood pressure. Identifying potential mechanisms of salt sensitivity in susceptible populations and linking them to protective or harmful dietary and lifestyle factors can lead to more specific guidelines for the prevention of hypertension and cardiovascular disease.