In many analytical chemical procedures, organic solvents are required to favour a better global yield upon the separation, extraction, or isolation of the target phytochemical analyte. The selection of extraction solvents is generally based on the solubility difference between target analytes and the undesired matrix components, as well as the overall extraction procedure cost and safety. Hansen Solubility Parameters are typically used for this purpose. They are based on the product of three coordinated forces (hydrogen bonds, dispersion, and dipolar forces) calculated for any substance to predict the miscibility of a compound in a pure solvent, in a mixture of solvents, or in non-solvent compounds, saving time and costs on method development based on a scientific understanding of chemical composition and intermolecular interactions. This review summarises how Hansen Solubility Parameters have been incorporated into the classical and emerging (or greener) extraction techniques of phytochemicals as an alternative to trial-and-error approaches, avoiding impractical experimental conditions and resulting in, for example, saving resources and avoiding unnecessary solvent wasting.