A common misunderstanding about Roman Catholic theology is that the Council of Trent (1545-1563) got rid of the doctrine of Indulgences. The truth, however, is that Trent removed much of the abuses of the doctrine. While many are unaware of this, Indulgences are still much a part of Roman Catholic theology, even post-Vatican II. The following comes from the 1994 Catechism of the Catholic Church:
X. INDULGENCES
1471 The doctrine and practice of indulgences in the Church are closely linked to the effects of the sacrament of Penance.
What is an indulgence?
"An indulgence is a remission before God of the temporal punishment due to sins whose guilt has already been forgiven, which the faithful Christian who is duly disposed gains under certain prescribed conditions through the action of the Church which, as the minister of redemption, dispenses and applies with authority the treasury of the satisfactions of Christ and the saints."
"An indulgence is partial or plenary according as it removes either part or all of the temporal punishment due to sin." The faithful can gain indulgences for themselves or apply them to the dead.
1472 To understand this doctrine and practice of the Church, it is necessary to understand that sin has a double consequence. Grave sin deprives us of communion with God and therefore makes us incapable of eternal life, the privation of which is called the "eternal punishment" of sin. On the other hand every sin, even venial, entails an unhealthy attachment to creatures, which must be purified either here on earth, or after death in the state called Purgatory. This purification frees one from what is called the "temporal punishment" of sin. These two punishments must not be conceived of as a kind of vengeance inflicted by God from without, but as following from the very nature of sin. A conversion which proceeds from a fervent charity can attain the complete purification of the sinner in such a way that no punishment would remain.
1473 The forgiveness of sin and restoration of communion with God entail the remission of the eternal punishment of sin, but temporal punishment of sin remains. While patiently bearing sufferings and trials of all kinds and, when the day comes, serenely facing death, the Christian must strive to accept this temporal punishment of sin as a grace. He should strive by works of mercy and charity, as well as by prayer and the various practices of penance, to put off completely the "old man" and to put on the "new man."
1474 The Christian who seeks to purify himself of his sin and to become holy with the help of God's grace is not alone. "The life of each of God's children is joined in Christ and through Christ in a wonderful way to the life of all the other Christian brethren in the supernatural unity of the Mystical Body of Christ, as in a single mystical person."
1475 In the communion of saints, "a perennial link of charity exists between the faithful who have already reached their heavenly home, those who are expiating their sins in purgatory and those who are still pilgrims on earth. between them there is, too, an abundant exchange of all good things." In this wonderful exchange, the holiness of one profits others, well beyond the harm that the sin of one could cause others. Thus recourse to the communion of saints lets the contrite sinner be more promptly and efficaciously purified of the punishments for sin.
1476 We also call these spiritual goods of the communion of saints the Church's treasury, which is "not the sum total of the material goods which have accumulated during the course of the centuries. On the contrary the 'treasury of the Church' is the infinite value, which can never be exhausted, which Christ's merits have before God. They were offered so that the whole of mankind could be set free from sin and attain communion with the Father. In Christ, the Redeemer himself, the satisfactions and merits of his Redemption exist and find their efficacy."
1477 "This treasury includes as well the prayers and good works of the Blessed Virgin Mary. They are truly immense, unfathomable, and even pristine in their value before God. In the treasury, too, are the prayers and good works of all the saints, all those who have followed in the footsteps of Christ the Lord and by his grace have made their lives holy and carried out the mission in the unity of the Mystical Body."
1478 An indulgence is obtained through the Church who, by virtue of the power of binding and loosing granted her by Christ Jesus, intervenes in favor of individual Christians and opens for them the treasury of the merits of Christ and the saints to obtain from the Father of mercies the remission of the temporal punishments due for their sins. Thus the Church does not want simply to come to the aid of these Christians, but also to spur them to works of devotion, penance, and charity.
1479 Since the faithful departed now being purified are also members of the same communion of saints, one way we can help them is to obtain indulgences for them, so that the temporal punishments due for their sins may be remitted.
A related document would be from January 1, 1967, issued by Pope Paul VI, "Indulgentiarum Doctrina" which affirms and clarifies this doctrine.
As Ludwig Ott, one of the leading Catholic theologians of the modern era, wrote on pages 441-42 of The Fundamentals of Catholic Dogma:
The Council of Trent declared against the attacks of Wycliffe and Luther: Sacrosancta synodus … eos anathemate damnat, qui (indulgentias) aut inutiles esse asserunt, vel eas concedendi in Ecclesia potestatem esse negant. D 989, 998 Cf. D 622, 676 et seq., 757 et seq.
Pope Leo X in the Indulgence Decretal “Cum postquam” (1518), bases the Church’s power to grant Indulgences on the power of the keys. This must not be understood as referring in the narrow sense to the power of forgiving sins, but rather as referring in the wider sense to the jurisdiction of the Church. Thus not every possessor of the power to forgive sins also possesses the power to grant Indulgences. The power to remit the temporal punishments for sins is not automatically included in the power to absolve from the guilt of sins and their eternal punishment. By its very nature an Indulgence is not a pure act of grace, in which the temporal punishment for sin is remitted gratis without anything being done in return: it implies compensation drawn from the treasury of satisfaction amassed by Christ and by the Saints. The Bishops of the Christian communion are entitled to distribute this spiritual treasure among the faithful. The possibility of vicarious satisfaction derives from the unity of the Mystical Body of Christ, the Communion of Saints. Accordingly, the power to give Indulgences rests both on the power of jurisdiction residing in the Church hierarchy and on the union of the faithful in the Communion of Saints. Cf. D 740a. Suppl. 25, 1.
The modern form of Indulgence developed in the 11th century. It emerged from the extra-sacramental absolutions of the early Middle Ages, in which the Pope, the bishops and the priests, frequently invoking the power of binding and loosing transferred to them, besought the mercy of God for individual persons or for the faithful generally with a view to the forgiveness of their sins. When in the 11th century, the forgiveness of sins which people hoped to be granted by God began to be imputed to the penance imposed by the Church absolution began to be regarded as an Indulgence. Even in Christian antiquity the Church exercised, in a different form, the power to grant Indulgences. In response to the intercessory appeals (Letters of Peace) of the Martyrs, the Church especially the Church of North Africa in the 3rd century (St. Cyprian), granted to individual penitents in specific cases, a partial remission of the penitential punishments imposed. People confidently expected that God would remit to them the remainder of the punishments for sins on the intercession and for the sake of the merits of the Martyrs. In the early Middle Ages, under the influence of Germanic legal opinions, the Redemptions (penitential absolutions) appeared, by which severe confession punishments were transformed into easier substitution—works (alms, pilgrimages). Even if fundamentally the equivalence of the commuted penance to the original penance was demanded, in fact the commutation meant an alleviation of the penance. In view of the Communion of Saints, helpers (monks) were permitted to assist in the performance of the penance, or a representative penance was allowed, especially in cases of sickness. This, of course, opened the door to the abolition of the ancient severe penances. The immediate preliminary fore-runners of Indulgences were the absolutions, current since the early Middle Ages, which were at first merely intercessions, but which later acquired more and more the character of an authoritative absolution.
Those Latter-day Saints who wish for some form of theological ecumenism with Rome should remember this and other doctrines (e.g., the Mass as a propitiatory sacrifice and Transubstantiation) that do not clarify, but sadly, perverts, the gospel of Jesus Christ.