Please follow the above link for a snazzy time line. Otherwise, the following is a quick summary of some of the highlights.
1914: Rubella is confirmed to be due to a viral infection, and also thus distinct from scarlet fever. The term "German Measles" is first used.
1938: EEV and WEV were first isolated from humans
1941: Congenital Rubella Syndrome first identified by Normann Gregg after a rubella outbreak
1952: Sindbis isolated
1962: Rubella Epidemic resulted in 30,000 still births and 20,000 deformities due to CRS
1963: RRV isolated
1969: Rubella vaccine is licensed
1972: MMR vaccine is licensed
1984: Togaviridae family was split into three: Togaviridae, Flaviviridae, and Pestiviridae
1998: New Zealand squashes Ross River Virus outbreaks by leading the eradication of the insect vector
2008: Chikungunya cases in Singapore following a series of outbreaks across the world (India, Australia, and Italy also witnessed cases)