The invention relates to a method for functionalizing natural fatty substances: According to said method, plant oils including at least two unsaturations and the derivatives thereof, fatty acids including at least one unsaturated compound and the derivatives thereof, and mixtures of same, are reacted with a thiol derivative of formula (I), at a temperature of between 0° C. and the temperature of total degradation of the natural fatty substance and in the presence of a thermal initiator compound or a redox initiator, or by UV radiation, or by UV radiation and in the presence of a photoinitiator. The invention also relates to the resulting functionalized fatty substances and to the use thereof for the preparation of polymers. The invention further relates to a method for preparing polymers from at least one functionalized fatty substance obtained by said functionalization method.