In 1931, Weimer reported that the causal agent of a mosaic disease of alfalfa was a virus, which he named alfalfa mosaic virus (AMV). This virus has subsequently received several other designations, including Alfalfa Virus I, Medicago Virus 2, Marmor rnedicaginis, and Lucerne Mosaic Virus, and R/1 1.3/18 U/U s/Ap. Various research workers have shown that this virus causes diseases in other crops, e.g., Potato Calico, noted by Hungerford. AMV was partially purified by Ross; thus it was the first aphid-transmitted virus to be purified. However, there was little interest in purified AMV until around 1960, when Bancroft and Kaesberg, Kelley and Kaesberg, and Gibbs et al., showed that virus preparations contain several components and that the virus particles, unlike those of other plant viruses, have a bacilliform shape, Subsequently, work on this virus has intensified with the studies on the structure and function of the components. This chapter is intended to bring together information on a wide range of topics and to offer some possible explanations of the unusual in vivo and in vitro behavior of this virus.