Drug function study is vital in current drug discovery, design, and development. Determining the drug functions of a novel drug is time-consuming, complicated, expensive, and requires many experts and clinical testing phases. The computational-based drug function prediction activity has recently become more attractive due to its capability to reduce drug development design complexity, time, human resources, cost, chemical waste, and the risk of failure. The evolution of the computational model has advanced as an effective tool for predicting and analyzing drug functions, which are derived from Medical Subject Headings (MeSH). However, predicting drug functions still faces several difficulties. Therefore, an exhaustive literature survey was conducted that discusses the application of computational methods to predict drug functions in the past decade. Additionally, this paper discusses the utilization of drug functions as an input feature to predict adverse drug reactions and disease classification. This work also provides an overview of the computational models with their performance, multi-label problem transformation methods, drug properties, and their sources needed for the task of drug function prediction. Finally, unsolved issues, research gaps, and difficulties with the drug function prediction task have been summarized.