Plant products and its by-products are rich source of bioactive compounds like antioxidants, flavonoids, phenolics, pigments and phytochemicals. Bioactive compound's health-promoting properties are well studied. However, optimal extraction of bioactive compounds is a complex, labour- and time-intensive process. It is also highly sensitive to experimental variables. Predicting output variables can reduce the experimental work and has positive environmental impact. Various tools such as Response Surface Methodology (RSM), Mathematical modelling have been commonly used for optimization and predictive modelling of the extraction process. Although mathematical modelling and RSM are efficient, recent studies have used Artificial Neural Network (ANN) which is more efficient and accurate and can perform extensive predictions with high accuracy. The manuscript focuses on current trends of ANN application in optimizing the extraction of bioactive compounds. In this study, ANN and RSM have been compared in terms of their performances in optimizing and modelling the extraction of bioactive compounds from herbs, medicinal plants, fruit, vegetables, and their by-products. The findings from the literature indicate that efficiency of ANN was superior to RSM. Future researches can focus on use of ANN in industrial optimization experiments.