They are the Taoist wizards from Yuldo and they have different abilities. The story begins when Kang Rim and Hong Moo Yeon killed most of the Yuldo citizens. Jeon Woo Chi almost died but he was saved by his master.
The story is quite interesting and there are many funny scenes / incidents when Jeon Woo chi aka Lee Chi tried his best to solve many mysteries happened in Joseon.
Cha Tae Hyun : Lee Chi / Jeon Woo Chi
Uee : Hong Moo Yeon (Hong Gil Dong's granddaughter)
Lee Hee Joon : Kang Rim
and the other supporting cast as you can find : http://wiki.d-addicts.com/Jeon_Woo_Chi
If you like historical drama (but this one is quite interesting), you should watch this drama.... :)