Hemodynamic monitoring technologies are evolving continuously—a large number of bedside monitoring options are becoming available in the clinic. Methods such as echocardiography, electrical bioimpedance, and calibrated/uncalibrated analysis of pulse contours are becoming increasingly common. This is leading to a decline in the use of highly invasive monitoring and allowing for safer, more accurate, and continuous measurements. The new devices mainly aim to monitor the well-known hemodynamic variables (e.g., novel pulse contour, bioreactance methods are aimed at measuring widely-used variables such as blood pressure, cardiac output). Even though hemodynamic monitoring is now safer and more accurate, a number of issues remain due to the limited amount of information available for diagnosis and treatment. Extensive work is being carried out in order to allow for more hemodynamic parameters to be measured in the clinic. In this review, we identify and discuss the main sensing strategies aimed at obtaining a more complete picture of the hemodynamic status of a patient, namely: (i) measurement of the circulatory system response to a defined stimulus; (ii) measurement of the microcirculation; (iii) technologies for assessing dynamic vascular mechanisms; and (iv) machine learning methods. By analyzing these four main research strategies, we aim to convey the key aspects, challenges, and clinical value of measuring novel hemodynamic parameters in critical care.