Computational and statistical tools help manage the prevailing challenges of the 17 Sustainable Development Goals (SDGs) by providing meticulous understanding of contemporary issues. However, complex challenges are difficult to handle with conventional techniques, resulting to the need for more advanced methods. Artificial neural networks (ANNs) are often used as an advanced approach in modelling complex behaviour of systems. Evaluating the current utilization of ANNs helps researchers gauge their applicability to SDG-related issues. The gaps among the studied SDGs need to be addressed through a comprehensive survey of the state-of-the-art literature. Hence, this work reviews published journal articles on the application of ANNs in resolving issues of the SDGs. This review identifies the current trends and limitations of ANN for SDG, and discusses its prominent applications and field of utilization. Descriptive and content analysis of journal articles is performed for this review. Journal articles from the Scopus database reveal Clean Water and Sanitation, Affordable and Clean Energy, Sustainable Cities and Communities, and Responsible Consumption and Production are the most popular subject matter for modelling and forecasting. New innovative functions include feature selection, kriging, and simulation. The main contribution of this work is a comprehensive mapping of the current state of this area of research. This work aims to aid future researchers to recognize further possible uses of ANNs with respect to the SDGs.