Cloud computing as a new computing model, provides computing and storage services to users by the virtualization technology. Users then can request and access elastic cloud resources on demand to run their applications via the Internet. Recently geo-distributed cloud has been a hot research topic in both academia and industry. It federates multiple cloud sites to maintain huge and distributed virtual resources, so as to provide better services for users. Based on fundamental research problems in geo-distributed cloud systems, this acticle describes the international and domestic research progress of this area, including architecture design, resource scheduling schemes, and security mechanisms. It also points out some of the research trends in the field.