[If you haven’t seen the predecessors, you can find them all here.]
Church growth during the 1960s and 70s placed increased pressure on the apostles in their role in local priesthood organization and regulation to say nothing of bureaucratic administration at headquarters. Stake conferences were reduced in number to 2 per year, the First Council, the Assistants and Regional Representatives were in place, but more help would be needed based on growth predictions. In 1975, the First Presidency and the Twelve made public the decision to reconstitute the First Quorum. The First Council would again be known as the Presidency of the Seventy. Three new men were called into the quorum and the first quorum was defined as a body of general authorities.
One year previous to this, seventies quorums were redistributed to stake jurisdictions, no longer would quorums cross stake boundaries. For some decades, stake presidents were authorized to use the seventies in various ways. Now they had them where they wanted them. The stake seventies presidencies were now the stake mission presidencies. The First Council’s role was again diminished in the lives of the quorums.
In 1976, the office of Assistant to the Twelve was abolished, and those high priests were ordained seventies and placed in the first quorum of the Seventy. A number of long-time First Council members expressed their joy over this move. But the return of the first quorum meant reloading it not with local seventies or elders but with men of wide experience in local leadership. The constituency of the Presidency of the Seventy would change, and the members of the old First Council gradually moved out of the presidency and into the first quorum.
Other changes were afoot. Term of service was about to become an issue. Membership in the First Council had been a lifetime call baring release for cause or promotion. Now that would change. It was experimental. At first it was announced that some members of the first quorum would be called in temporary 3-5 year service. Then a second quorum of seventy (also general authorities — 1989) was opened and its membership contained these men with limited time of service. An “Emeritus status” was then approved and it was announced that members of the first quorum would retire to that status as needed. Finally a firm maximum date of 70 years of age was confirmed. Health concerns might speed the date of emeritus status. The point here was to maintain a vigorous membership that could not be crippled by age or health as so often was the case in the First Presidency and Twelve and to provide a larger selection of men the opportunity to serve.
In 1997 the previously announced “Area Authorities” (effectively replacing the Regional Representatives – See President Gordon B. Hinckley’s explanation here.) were brought into the fold and ordained as seventies. Eventually their title moved to “Area Seventy” and the number of quorums increased to eight in 2005. In 2010, their authority was enhanced from advisory status and “by assignment” supervision to one of “line” authority. It will be interesting to see what further evolution comes to the office.
On a final note, in the October 1986 General Priesthood session of the LDS General Conference, President Ezra Taft Benson announced that seventies quorums in stakes were discontinued and seventies in stakes would now join with the elders quorums. The policy continued the 1901 effected reduction in the need for local seventies quorums.
I’m curious. Are there any seventies out there from that era, never ordained high priests? Fess up if you know someone in this category.
 Fixed quorum membership had been abolished long before. When you moved, you joined the quorum in your new location at least by 1884. The policy was tweaked from time to time. Stake presidents were now (1974) authorized to ordain seventies, with First Council approval.
 “Line” authority means an officer is in the chain of command so to speak. Such officers have defined decision-making boundaries which determine what issues have to be passed up the chain and which they can decide themselves. Mission presidents within the U.S. for example now are under the supervision of an Area Seventy, whereas previous to this the AS functioned in a council advisory capacity. Same with stake and temple presidents I think. (One man described to me his tour as mission president as the time when he had a thousand bosses.)