The term "Iaido" was created early in the 20th century by Nakayama Hakudo. Before then it was refered to as Batto, Batto-Justsu or Saya No Uchi and is perhaps the 2nd oldest still existing martial art in Japan.

The foundations of the two main styles, Eishin Ryu and Muso Shinden Ryu style of Iaido can be traced back around 450 years ago to Hayashizaki Jinsuke Minanoto Shigenobu. Hayashizaki Jinsuke(1546 - 1621) lived in what is now modern day Kanagawa where he established his own style of sword drawing; Shimmei Muso Ryu. 
Each generation a headmaster or "soke" is apointed to continue on the traditions and to contribute thier own style to the art. 
After the 11th generation there was a split in linage to leading to Saito Iamau, the eighteenth generation soke of the Muso Shinden Ryu and Ikeda Takashi Seiko the 22nd generation Eishin Ryu Soke.

Today Muso Jikiden Eishin Ryu ("Peerless, Direct Transmission, True-Faith Style") is one of the most widely practiced forms of Iaido.
It is widely accepted that the Eishin Ryu style derives its name from the 7th generation soke, Hasegawa Chikaranosuke Eishin as both the characters in his name and the Eishin style are the one and the same.