Blood pressure (BP) is one of the most important monitoring parameters in clinical medicine. For years, the cuff-based sphygmomanometer and the arterial invasive line have been the gold standards for care professionals to assess BP. During the past few decades, the wide spread of the oscillometry-based BP arm or wrist cuffs have made home-based BP assessment more convenient and accessible. However, the discontinuous nature, the inability to interface with mobile applications, the relative inaccuracy with movement, and the need for calibration have rendered those BP oscillometry devices inadequate for next-generation healthcare infrastructure where integration and continuous data acquisition and communication are required. Recently, the indirect approach to obtain BP values has been intensively investigated, where BP is mathematically derived through the "Time Delay" in propagation of pressure waves in the vascular system. This holds promise for the realization of cuffless and continuous BP monitoring systems, for both patients and healthy populations in both inpatient and outpatient settings. This review highlights recent efforts in developing these next-generation blood pressure monitoring devices and compares various mathematical models. The unmet challenges and further developments that are crucial to develop "Time Delay"-based BP devices are also discussed.