Viruses were discovered at the end of the 19th century. In 1892, Dimitri Ivanovsky, a Rusian botanist, discovered that the sap from tobacco plants affected by mosaic diseases could be passed through filters so fine as to exclude all known bacteria and still retain the ability to produce the diseases in new plants. In 1898, Frederich Loeffler and Paul Frosch reported similar results for the infectious agent of foot-and-mouth diseases of cattle. They also showed that an animal inoculated with a tiny amount of filtered material could itself subsequently give rise to a very potent inoculums.
More detail click Virus History