We develop new efficient algorithms for accurate prediction of two-phase/multiphase (solid, liquid, vapor) equilibria and physical properties of complex chemical systems, of interest to industrial and environmental applications. Our algorithms provide robust predictions for challenging types of equilibria, including open-ended dew lines with multiple critical points, double retrograde behaviour. Moreover, our algorithms can also be applied to calculate at will the lower/upper pressure or low/high temperature bubble or dew point parts of phase diagrams, thus being robust tools when retrograde regions are considered. Recently, a new algorithm was proposed for liquid - liquid equilibria of electrolyte solutions that account explicitly for the electroneutrality of the phases.