The Bunyavirales order is one of the largest groups of segmented negative-sense single-stranded RNA viruses, which includes many pathogenic strains that cause severe human diseases. The RNA segments of the bunyavirus genome are separately encapsidated by multiple copies of nucleoprotein (N), and both termini of each N-encapsidated genomic RNA segment bind to one copy of the viral L polymerase protein. The viral genomic RNA, N and L protein together form the ribonucleoprotein (RNP) complex that constitutes the molecular machinery for viral genome replication and transcription. Recently, breakthroughs have been achieved in understanding the architecture of bunyavirus RNPs with the determination of the atomic structures of the N and L proteins from various members of this order. In this review, we discuss the structures and functions of these bunyavirus RNP components, as well as viral genome replication and transcription mechanisms.