Exorcism
In Catholic Christianity, exorcisms are performed in the name of Jesus Christ. A distinction is made between a formal exorcism, which can only be conducted by a priest during a baptism or with the permission of a bishop, and "prayers of deliverance" which can be said by anyone.
The Catholic rite for a formal exorcism, called a "Major Exorcism", is given in Section 11 of the Rituale Romanum. The Ritual lists guidelines for conducting an exorcism, and for determining when a formal exorcism is required. Priests are instructed to carefully determine that the nature of the affliction is not actually a psychological or physical illness before proceeding.
Exorcist
The rite of conferral continues in societies that use the 1962 (or earlier) form of the Roman Rite, such as the Priestly Fraternity of St Peter, Society of St. Pius X, and also among groups not in communion with the current Bishop of Rome, such as the Society of St Pius V. Some believe that attainment of the position of Acolyte in post-Council practices implies ordination to the minor orders which used to be below it, such as Exorcist and Porter, although this has not been officially defined (although Canon Law section 1009 does specifically state that the only "orders are the episcopate, the priesthood and the diaconate").