The global pandemic of coronavirus disease 2019 (COVID-19), caused by severe acute respiratory syndrome coronavirus 2, has led to a dramatic loss of human life worldwide. Despite many efforts, the development of effective drugs and vaccines for this novel virus will take considerable time. Artificial intelligence (AI) and machine learning (ML) offer promising solutions that could accelerate the discovery and optimization of new antivirals. Motivated by this, in this paper, we present an extensive survey on the application of AI and ML for combating COVID-19 based on the rapidly emerging literature. Particularly, we point out the challenges and future directions associated with state-of-the-art solutions to effectively control the COVID-19 pandemic. We hope that this review provides researchers with new insights into the ways AI and ML fight and have fought the COVID-19 outbreak.