The beginning of 2020 has seen the emergence of coronavirus outbreak caused by a novel virus called SARS-CoV-2. The sudden explosion and uncontrolled worldwide spread of COVID-19 show the limitations of existing healthcare systems in timely handling public health emergencies. In such contexts, innovative technologies such as blockchain and Artificial Intelligence (AI) have emerged as promising solutions for fighting coronavirus epidemic. In particular, blockchain can combat pandemics by enabling early detection of outbreaks, ensuring the ordering of medical data, and ensuring reliable medical supply chain during the outbreak tracing. Moreover, AI provides intelligent solutions for identifying symptoms caused by coronavirus for treatments and supporting drug manufacturing. Therefore, we present an extensive survey on the use of blockchain and AI for combating COVID-19 epidemics. First, we introduce a new conceptual architecture which integrates blockchain and AI for fighting COVID-19. Then, we survey the latest research efforts on the use of blockchain and AI for fighting COVID-19 in various applications. The newly emerging projects and use cases enabled by these technologies to deal with coronavirus pandemic are also presented. A case study is also provided using federated AI for COVID-19 detection. Finally, we point out challenges and future directions that motivate more research efforts to deal with future coronavirus-like epidemics.