Maintaining an optimal blood pressure (BP) during shock is a fundamental tenet of critical care. Optimal BP targets may be different for different patients. In current practice, too often, uniform BP targets are pursued which may result in inadvertently accepting a degree of untreated relative hypotension, i.e., the deficit between patients’ usual premorbid basal BP and the achieved BP, during vasopressor support. Relative hypotension is a common but an under-recognized and an under-treated sign among patients with potential shock state. From a physiological perspective, any relative reduction in the net perfusion pressure across an organ (e.g., renal) vasculature has a potential to overwhelm autoregulatory mechanisms, which are already under stress during shock. Such perfusion pressure deficit may consequently impact organs’ ability to function or recover from an injured state. This review discusses such pathophysiologic mechanisms in detail with a particular focus on the risk of new-onset acute kidney injury (AKI). To review current literature, databases of Medline, Embase, and Google scholar were searched to retrieve articles that either adjusted BP targets based on patients’ premorbid BP levels or considered relative hypotension as an exposure endpoint and assessed its association with clinical outcomes among acutely ill patients. There were no randomized controlled trials. Only seven studies could be identified and these were reviewed in detail. These studies indicated a significant association between the degree of relative hypotension that was inadvertently accepted in real-world practice and new-onset organ dysfunction or subsequent AKI. However, this is not a high-quality evidence. Therefore, well-designed randomized controlled trials are needed to evaluate whether adoption of individualized BP targets, which are initially guided by patient's premorbid basal BP and then tailored according to clinical response, is superior to conventional BP targets for vasopressor therapy, particularly among patients with vasodilatory shock states.