In 1883 Adolf Mayer first described the disease that could be transferred between plants, similar to bacterial infection. However, in 1889, Martinus Beijerinck showed that a filtered, bacteria-free culture medium still contained the infectious agent. First concrete evidence for its existence was given by Dmitri Ivanowski in 1892. In 1935, Wendell Meredith Stanley crystallized the virus for electron microscopy and showed that it remains active even after crystallization. For his work, he was awarded 1/4 of the Nobel Prize in Chemistry in 1946. In 1955, Heinz Fraenkel-Conrat and Robley Williams showed that purified TMV RNA and its capsid (coat) protein assemble by themselves to functional viruses, indicating that this is the most stable structure (the one with the lowest free energy), and likely the natural assembly mechanism within the host cell.
Tobacco mosaic virus has a rod-like appearance. Its capsid is made from a single protein that assembles itself around the viral RNA in a helical structure (16.3 proteins per helix turn).
TMV's RNA sequence has been published in "American Chemical Society's Chemical Abstracts" in 1972 as a single word, Acetylseryltyrosylserylisol...serine, which supposedly is the longest word in the English language.