Natural compounds have a high potential for the treatment of various conditions, including infections, inflammatory diseases, and cancer. However, they usually present poor pharmacokinetics, low specificity, and even toxicity, which limits their use. Therefore, targeted drug delivery systems, typically composed of a carrier and a targeting ligand, can enhance natural product selectivity and effectiveness. Notably, aptamers—short RNA or single-stranded DNA molecules—have gained attention as promising ligands in targeted drug delivery since they are simple to synthesize and modify, and they present high tissue permeability, stability, and a wide array of available targets. The combination of natural products, namely plant-based compounds, with a drug delivery system utilizing aptamers as targeting agents represents an emerging strategy that has the potential to broaden its applications. This review discusses the potential of aptamers as targeting agents in the delivery of natural compounds, as well as new trends and developments in their utilization in the field of medicine.