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 to timely handle public health emergencies. In such contexts, innovative technologies such as blockchain and Artificial Intelligence (AI) have emerged as promising solutions for fighting coronavirus epidemic. On the one hand, blockchain can combat pandemics by enabling early detection of outbreaks, protecting user privacy, and ensuring reliable medical supply chain during the outbreak tracking. On the other hand, AI provides intelligent solutions for identifying symptoms caused by coronavirus for treatments and supporting drug manufacturing. Motivated by these, in this paper we present an extensive survey on the use of blockchain and AI for combating coronavirus (COVID-19) epidemics based on the rapidly emerging literature. First, we introduce a new conceptual architecture which integrates blockchain and AI specific for COVID-19 fighting. Particularly, we highlight the key solutions that blockchain and AI can provide to combat the COVID-19 outbreak. Then, we survey the latest research efforts on the use of blockchain and AI for COVID-19 fighting in a wide range of applications. The newly emerging projects and use cases enabled by these technologies to deal with coronavirus pandemic are also presented. Finally, we point out challenges and future directions that motivate more research efforts to deal with future coronavirus-like epidemics.