To synthesize physiological principles and practical monitoring strategies for perioperative and intensive care hemodynamics, addressing two questions: which variables should be monitored, and what targets should be pursued to optimize outcomes. The review is educational in scope and highlights instrumentation details and clinical applications.Narrative, physiology-anchored review of oxygen delivery, venous return (VR), and regulation of mean arterial pressure (MAP) as a derived target. Reviews for educational purposes are included, with emphasis on instrumentation principles and clinical use cases. Invasive and non-invasive modalities are compared. Evidence from goal-directed therapy (GDT) trials in operating room and intensive care contexts is summarized to link physiology with therapy.(1) adequacy of oxygen delivery cannot be judged from MAP alone; MAP reflects the interaction of cardiac output (CO), systemic vascular resistance (SVR), and right atrial pressure. (2) VR depends on effective circulating volume, venous compliance, and mean systemic filling pressure. (3) Microcirculatory assessment remains limited; macrocirculatory surrogates and biomarkers provide guidance but have constraints. (4) Device outputs labeled identically are not interchangeable; calibration strategy and physiological assumptions are decisive. (5) GDT improves processes and may benefit selected high-risk patients, but large trials show mixed effects on mortality.Effective hemodynamic management requires physiology-based reasoning: identify the limiting factor, then select monitoring tools and therapeutic targets accordingly. MAP must be interpreted with CO, SVR, and RAP. Individualized, dynamic targets and trend-based responses outperform fixed thresholds. Embedding ultrasound skills, fluid-responsiveness testing, and calibrated device interpretation are levers to translate monitoring into safer care.