Throughtout in history, several shinobi, jinchuriki or not, have demonstrated the ability to gain control of the tailed beasts. The cause and effect of this control varies between capable of doing it. However, only six people are known to have full control of the tailed beasts' power: Hashirama Senju, Madara Uchiha, Hanaku Senju, Sazaku Uchiha, Yagura, and Killer Bee.
When a jinchuriki has a strong relationship with his/her tailed beast, the beast can act as his/her partner in battle. Jinchuriki who have complete control and co-operation over with the tailed beasts within them, are immune to genjutsu, as they can disturb the jinchuriki's chakra flow to break genjutsu.
Hashirama Senju, the First Hokage, and his son, Hanaku Senju, could control the tailed beasts using the Hokage Style Elder Jutsu: Tenth Edict On Elightment, which utilizes the power of their clan's Wood Style kekkei genkai to forcibly suppress the tailed beasts' chakra.
Madara Uchiha and his nephew, Sazaku Uchiha, two former leaders of the Uchiha Clan, using their own Mangekyo Sharingan to subdue the tailed beasts, and done it at least twice. When Madara has to control the Nine-Tails, he focues on the beast's eyes, and the Sharingan will appear over them, and then the Sharingan's tomoe disappears as the pupil enlarges. And had also used of the Sharingan against a tailed beast within the jinchuriki's subconscious, but only to supress its chakra.