This dissertation addresses the anomalous properties of water at high temperatures near the vapor-liquid critical point and at low temperatures in the supercooled liquid region. The first part of the dissertation is concerned with the concentration dependence of the critical temperature, density, and pressure of an aqueous sodium chloride solution. Because of the practical importance of an accurate knowledge of critical parameters for industrial, geochemical, and biological applications, an empirical equation for the critical locus of aqueous sodium chloride solutions was adopted in 1999 by the International Association for the Properties of Water and Steam (IAPWS) as a guideline. However, since this original Guideline on the Critical Locus of Aqueous Solutions of Sodium Chloride was developed, two new theoretical developments occurred, motivating the first part of this dissertation. Here, I present a theory-based formulation for the critical parameters of aqueous sodium chloride solutions as a proposed replacement for the empirical formulation currently in use. This formulation has been published in the International Journal of Thermophysics and recommended by the Executive Committee of IAPWS for adoption as a Revised Guideline on the Critical Locus of Aqueous Solutions of Sodium Chloride. The second part of the dissertation addresses a new concept, considering cold water as a supercritical solvent. Based on the idea of a second, liquid-liquid, critical point in supercooled water, we explore the possibility of supercooled water as a novel supercooled solvent through the thermodynamics of critical phenomena. In 2006, I published a Physical Review letter presenting a parametric scaled equation of state for supercooled-water. Further developments based on this work led to a phenomenological mean-field "two-state" model, clarifying the nature of the phase separation in a polyamorphic single-component liquid. In this dissertation, I modify this two-state model to incorporate solutes. Critical lines emanating from the pure-water critical point show how even small additions of solute may significantly affect the thermodynamic properties and phase behavior of supercooled aqueous solutions. Some solutes, such as glycerol, can prevent spontaneous crystallization, thus making liquid-liquid separation in supercooled water experimentally accessible. This work will help in resolving the question on liquid polyamorphism in supercooled water.