A litany is a prayerful sequence of supplications which are intoned by a deacon or priest in the name of all those praying. After each petition the choir or people sing, "Lord, have mercy," "Grant this, O Lord" (or in some translations, "Grant it, O Lord"), or "To Thee, O Lord" (or "To You, O Lord").
Each litany concludes with an exclamation (doxology) said by the priest glorifying the Holy Trinity.
The Great Litany, or Litany of Peace, begins with the words "In peace, let us pray to the Lord." It is typically found near the beginning of services. It contains many different petitions for prosperity and salvation of God's people.
The Little Litany is a shortened form of the Great Litany. It begins with the words: "Again and again in peace let us pray to the Lord," and contains only three petitions.
Litany of Supplication
The Litany of Supplication is characterized by its first petition, "Let us complete our prayer unto the Lord," and by its petitions that end with "let us ask of the Lord," to which the faithful respond "Grant this, O Lord." The petitions beseech ("supplicate") the Lord for the spiritual well-being of the faithful. The initial petition may be modified to denote time of day (e.g. "Let us complete our evening prayer unto the Lord."), and therefore the Litany of Supplication may be called the "Evening Litany" or "Morning Litany," depending on the service in which it is said. In the Divine Liturgy, which is considered to be "outside of time," the Litany of Supplication does not denote a time of day.
Litany of Fervent Supplication
The Litany of Fervent Supplication is characterized by the three-fold "Lord, have mercy," thus giving it its name of Fervent. It is in this litany that the people pray for their own particular needs, as well as those of the entire Church, their neighbors, their country, and the entire world.
The Augmented Litany is so called because it consists of the petitions contained in the Litany of Fervent Supplication, augmented by two petitions at the beginning: "Let us say with all our soul and with all our mind, let us say:" and "O Lord Almighty, the God of our Fathers, we pray Thee, hearken and have mercy." The responses to these augmented petitions, unlike those taken from the Litany of Fervent Supplication, consist of a single "Lord have mercy," instead of three. The Augmented Litany may also be "augmented" with special petitions at times of need, such as for peace at times of war, for the health of a graevely-ill parishioner, the blessing of a new Marriage, etc.
Litany for the Departed
The Litany for the Departed is composed of entreaties to the Lord, that He might grant rest in the Heavenly Kingdom to the souls of the departed by forgiving them all their sins. It may be inserted into the Divine Liturgy, immediately following the Augmented Litany, especially at funerals and on Soul Saturdays, but also for the newly-departed, however never on a day of the Resurrection (i.e. Paschal-tide & Sundays).
Litany for the Catechumens
The Litany for the Catechumens contains petitions, offered by the Orthodox faithful, for the catechumens of the Church. These petitions ask the Lord to guide the catechumens in their journey toward "Illumination" in the Orthodox faith. The Litany for the Catechumens is found in the Divine Liturgy, and is immediately followed by the first Litany of the Faithful.
Litany of the Faithful
The first Litany of the Faithful dismisses the catechumens. At one time it was common for those who were not going to receive the Eucharist (among them the Catechumens) to move to the back of the church, or leave the building altogether, at the time of the Liturgy of the Faithful. The second Litany of the Faithful is usually abbreviated as a Little Litany when no deacon is serving, but normally contains several petitions from the Great Litany. The Litanies of the Faithful uniquely contain the exclamation, "Wisdom," just prior to their respective doxologies.