Christus Dominus (abbreviation "CD") is the Second Vatican Council's Decree on the Pastoral Office of Bishops. It was approved by a vote of 2,319 to 2 of the assembled bishops and was promulgated by Pope Paul VI on 28 October 1965. The title in Latin means "Christ the Lord" and is from the first line of the decree, as is customary for Roman Catholic documents. Christus Dominus calls for strong episcopal conferences of bishops, to set the standard for the church in their region, while fully supporting the Vatican and the Pope.  (The full text in English is available from the Holy See's website.)
CD describes how bishops exercise their office at three levels: in the universal church (chapter one), in their own "particular church" or diocese (chapter two), and at the regional or national level (chapter three).
The First Vatican Council of 1869-1870 focused on the pope and defined the doctrine of "papal infallibility" but it never got around to saying anything about the other bishops. Thus, when Pope John XXIII called for a Second Vatican Council, everyone expected it to take up this unfinished business.
The role of the bishops of the church was brought into renewed prominence, especially when seen collectively, as a college that has succeeded to that of the apostles in teaching and governing the church. This college does not exist without its head, the successor of St. Peter.
In these days especially bishops frequently are unable to fulfill their office effectively and fruitfully unless they develop a common effort involving constant growth in harmony and closeness of ties with other bishops. Episcopal conferences already established in many nations-have furnished outstanding proofs of a more fruitful apostolate. Therefore, this sacred synod considers it to be supremely fitting that everywhere bishops belonging to the same nation or region form an association which would meet at fixed times. Thus, when the insights of prudence and experience have been shared and views exchanged, there will emerge a holy union of energies in the service of the common good of the churches. (CD 37)
Accordingly, claims made by some, that the council gave the church two separate earthly heads, the College of Bishops and the Pope, were countered by the Preliminary Explanatory Note added to the Dogmatic Constitution on the Church Lumen Gentium and printed at the end of the text.
This Note states:
There is no such thing as the college without its head ... and in the college the head preserves intact his function as Vicar of Christ and pastor of the universal Church. In other words it is not a distinction between the Roman Pontiff and the bishops taken together, but between the Roman Pontiff by himself and the Roman Pontiff along with the bishops.
In many countries, bishops already held regular conferences to discuss common matters. The council required the setting up of such episcopal conferences, entrusting to them responsibility for the necessary adaptation to local conditions of general norms. Certain decisions of the conferences have binding force for individual bishops and their dioceses, but only if adopted by a two-thirds majority and confirmed by the Holy See.
Regional conferences, such as the CELAM, exist to assist in promoting common action on a regional or continental level, but do not have even that level of legislative power.
After the publication of Humanae vitae in 1968, several problems emerged with the notion of collegiality promoted in the document. The fact that several episcopal conferences would openly rebel against the Pope had been unthinkable during the papacy of Pius XII. Prominent members in the Roman Curia deplored the fact that conference leaders appeared to behave as if they were regional popes. This complaint is notably found in the 1985 Ratzinger Report, a series of interviews where Cardinal Joseph Ratzinger deplores the lack of structure, organization and coordination between Rome and the local assemblies of Catholic bishops.