Despite the myriad peer-reviewed papers demonstrating novel Artificial Intelligence (AI)-based solutions to COVID-19 challenges during the pandemic, few have made significant clinical impact. The impact of artificial intelligence during the COVID-19 pandemic was greatly limited by lack of model transparency. This systematic review examines the use of Explainable Artificial Intelligence (XAI) during the pandemic and how its use could overcome barriers to real-world success. We find that successful use of XAI can improve model performance, instill trust in the end-user, and provide the value needed to affect user decision-making. We introduce the reader to common XAI techniques, their utility, and specific examples of their application. Evaluation of XAI results is also discussed as an important step to maximize the value of AI-based clinical decision support systems. We illustrate the classical, modern, and potential future trends of XAI to elucidate the evolution of novel XAI techniques. Finally, we provide a checklist of suggestions during the experimental design process supported by recent publications. Common challenges during the implementation of AI solutions are also addressed with specific examples of potential solutions. We hope this review may serve as a guide to improve the clinical impact of future AI-based solutions.