The family Bunyaviridae of segmented, negative-stranded RNA viruses includes over 350 members that infect a bewildering variety of animals and plants. Many of these bunyaviruses are the causative agents of serious disease in their respective hosts, and are classified as emerging viruses because of their increased incidence in new populations and geographical locations throughout the world. Emerging bunyaviruses, such as Crimean-Congo hemorrhagic fever virus, tomato spotted wilt virus and Rift Valley fever virus, are currently attracting great interest due to migration of their arthropod vectors, a situation possibly linked to climate change. These and other examples of continued emergence suggest that bunyaviruses will probably continue to pose a sustained global threat to agricultural productivity, animal welfare and human health. The threat of emergence is particularly acute in light of the lack of effective preventative or therapeutic treatments for any of these viruses, making their study an important priority. This review presents recent advances in the understanding of the bunyavirus life cycle, including aspects of their molecular, cellular and structural biology. Whilst special emphasis is placed upon the emerging bunyaviruses, we also describe the extensive body of work involving model bunyaviruses, which have been the subject of major contributions to our overall understanding of this important group of viruses.