Since determining experimentally a wide variety of thermophysical properties - even for a very small portion of the already known room temperature ionic liquids ( and their mixtures and solutions) - is an impossible goal, it is imperative that reliable predictive methods be developed. In turn, these methods might offer us clues to understanding the underlying ion - ion and ion - molecule interactions. 1-Butyl-3-methylimidazolium tetrafluoroborate, one of the most thoroughly investigated ionic liquids, together with water, the greenest of the solvents, have been chosen in this work in order to use their mixtures as a case study to model other, greener, ionic liquid aqueous solutions. We focus our attention both on very simple methodologies that permit one to calculate accurately the mixture's molar volumes and heat capacities as well as more sophisticated theories to predict excess properties, pressure and isotope effects in the phase diagrams, and anomalies in some response functions to criticality, with a minimum of information. In regard to experimental work, we have determined: ( a) densities as a function of temperature (278.15 <T/ K <333.15), pressure ( 1 <p/bar <600), and composition (0 <x(IL) <1), thus also excess molar volumes; (b) heat capacities and excess molar enthalpies as a function of temperature ( 278.15 <T/ K <333.15) and composition ( 0 <xIL <1); and ( c) liquid - liquid phase diagrams and their pressure ( 1 <p/ bar <700) and isotopic (H2O/D2O) dependences. The evolution of some of the aforementioned properties in their approach to the critical region has deserved particular attention.