Incremental forming (IF) is one of the novel manufacturing processes that has gained much attention from researchers and practitioners. As a result, various analytical and numerical models of IF have been developed. The remarkable thing is that artificial intelligence (AI)-based computational methods have been used in solving IF-related problems. This study reviews the extant literature relevant to IF. It is found that AI techniques such as artificial neural networks, support vector regression, decision trees, fuzzy logic, genetic algorithms, particle swarm optimization have been used in solving IF-relevant problems. In addition, hybrid methods that combine some of the above-mentioned techniques have also been used. Moreover, it is shown that the performance parameters of IF such as springback and geometrical accuracy, formability, forming forces, surface roughness, forming time, and average deformed sheet thickness have been predicted and a few toolpath strategies have been developed using AI-based techniques. Thus, this study would serve researchers and practitioners who want to solve IF-related problems and advance the applicability of IF.