Drug discovery and development is a complex and costly process. Machine learning approaches are being investigated to help improve the effectiveness and speed of multiple stages of the drug discovery pipeline. Of these, those that use Knowledge Graphs (KG) have promise in many tasks, including drug repurposing, drug toxicity prediction and target gene–disease prioritization. In a drug discovery KG, crucial elements including genes, diseases and drugs are represented as entities, while relationships between them indicate an interaction. However, to construct high-quality KGs, suitable data are required. In this review, we detail publicly available sources suitable for use in constructing drug discovery focused KGs. We aim to help guide machine learning and KG practitioners who are interested in applying new techniques to the drug discovery field, but who may be unfamiliar with the relevant data sources. The datasets are selected via strict criteria, categorized according to the primary type of information contained within and are considered based upon what information could be extracted to build a KG. We then present a comparative analysis of existing public drug discovery KGs and an evaluation of selected motivating case studies from the literature. Additionally, we raise numerous and unique challenges and issues associated with the domain and its datasets, while also highlighting key future research directions. We hope this review will motivate KGs use in solving key and emerging questions in the drug discovery domain.