Tiddlywinks (or TIDDLEDY WINKS as it was known at the time) was an incredible craze in the 1890s. Check out Rick Tucker’s article, Tiddlywinks: The Classic Victorian Pastime: On Target for the 21st Century for further information on the origins and early history of the game. The Tiddlywinks Game Catalog, with a complete listing of all known tiddlywinks games, also sheds illumination on the game through the past century or so.
Competitive tiddlywinks in the modern era originated at Cambridge University in 1954 (although precursors are known at Cambridge in 1947 and even before). Guy Consterdine authored the seminal history of the origins of competitive tiddlywinks, On the Mat (1954 to 1958), and also Winks Rampant (1958) about the expansion of winks to UK-wide public recognition. In 1962, Oxford toured the US, and a number of US collegiate teams were formed. Severin Drix reports on the early years of NATwA and Fred Shapiro reports on the history of US winks overall.
A detailed chronology of tiddlywinks is also available.