A CATHOLIC EXPLANATION OF ANATHEMA
from Nazareth Website
Anathemas per se are not used today, since the 1983 Code of Canon Law (CIC) abolished the canonical penalty of anathema, which was a form of excommunication. (Anathema meant something else in the Bible, but Trent was using it in its canon law sense).
This does not mean that the Church no longer believes those things. The formula "let him be anathema" is a traditional expression that ecumenical councils (all the way back to the first ecumenical council--Nicaea I--which defined the divinity of Christ) have used when making infallible definitions. Therefore, even if the canonical penalty of anathema no longer exists, this does not "undo" the infallible definitions expressed in Trent's canons. An infallible definition, by its very nature, can never be "undone." Therefore, the Church still believes and teaches all the infallible definitions Trent issued.
Furthermore, even though a person no longer incurs anathema by violating the canons of Trent, he may still incur excommunication. Many of Trent's definitions concern articles of faith, and for a Catholic to culpably doubt or deny them constitutes heresy (CIC 751), which in turn incurs excommunication (CIC 1364 §1).
Thus, while the canons of Trent may no longer lead to the specific penalty of anathema, they are still infallible and still can lead to the more general penalty of excommunication.