The recovery of bioactive compounds from plant and marine biomass still depends heavily on volatile organic solvents whose toxicity, flammability and environmental persistence sit awkwardly beside a pharmaceutical industry that increasingly measures itself against sustainability targets. Three classes of alternative solvent have moved from curiosity to credible replacement over the past two decades: deep eutectic solvents and their natural subclass, ionic liquids, and supercritical carbon dioxide. Each rests on a different physical principle, and each therefore succeeds and fails against a different part of the extraction problem. This review compares the three head to head across the dimensions that decide whether a solvent reaches a manufacturing plant rather than a single publication: extraction efficiency and selectivity, green-chemistry credentials, solute recovery, scalability and capital cost, and regulatory acceptability. The central argument is that no single class is universally superior, and that framing the three as competitors obscures how neatly their strengths partition by target polarity and production scale. Deep eutectic solvents, and especially natural deep eutectic solvents, dominate the recovery of polar phenolics and offer the most convincing green profile, but pay for it in viscosity and difficult product isolation. Ionic liquids provide selectivity and tunability that neither rival matches, yet a debated toxicity record, high cost and awkward recovery keep most applications at laboratory scale. Supercritical carbon dioxide delivers solvent-free, food-grade nonpolar extracts at industrial scale but is largely blind to hydrophilic solutes without a co-solvent. The field's most productive direction is not the search for one winner but the deliberate pairing of these solvents with each other and with intensification techniques, supported by the life-cycle accounting that green claims currently lack.