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The capacity to discriminate safe from dangerous compounds has played an important role in the evolution of species, including human beings. Highly evolved senses such as taste receptors allow humans to navigate and survive in the environment through information that arrives to the brain through electrical pulses. Specifically, taste receptors provide multiple bits of information about the substances that are introduced orally. These substances could be pleasant or not according to the taste responses that they trigger. Tastes have been classified into basic (sweet, bitter, umami, sour and salty) or non-basic (astringent, chilling, cooling, heating, pungent), while some compounds are considered as multitastes, taste modifiers or tasteless. Classification-based machine learning approaches are useful tools to develop predictive mathematical relationships in such a way as to predict the taste class of new molecules based on their chemical structure. This work reviews the history of multicriteria quantitative structure-taste relationship modelling, starting from the first ligand-based (LB) classifier proposed in 1980 by Lemont B. Kier and concluding with the most recent studies published in 2022.