The two main classical styles (koryu) of iaido practiced worldwide are Muso Jikiden Eishin-ryu and Muso Shinden-ryu. They resemble each other quite strongly because they branched off from one style sometime in the 17th century.
There are several branches of Muso Jikiden Eishin-ryu (MJER) that are practised today. One person who is considered to be a headmaster is Miura Takeyuki Hidefusa, who holds a 9th dan in MJER.
There are several lines of transmission extant for Muso Shinden-ryu also. One of them claims Mitsuzuka Takeshi as the headmaster, second one (those who are affiliated with Nippon Iaido Kyokai) regard Takada Gakudo as their head teacher.
