Recently the Church web site, lds.org ran a three part series (with President Boyd K. Packer and President Ronald A. Rasband) on the Seventy and their current relationship with the Twelve Apostles. That got me thinking about this group of Church leaders and with conference coming, it seemed appropriate to talk about them a little.
The Seventy form a uniquely Mormon approach to administration (the number has always been linked to the New Testament seventy — Luke 10). They were a part of the priesthood expansion/definition movement of the later Kirtland period. Doctrine and Covenants 107 introduces the office in LDS scripture but it does not reappear in the revelations. [Correction: note D&C 124:138-140 as per J. Stapley's comment below. Confirms the status of the Seventy as travelers.]
D&C 107 defines the position of the Seventy as resting in a family of priesthood groupings, each “equal in authority” to the others. That list of groupings:
1. The First Presidency
2. The Twelve Apostles
3. The Seventy
4. The High Council in Zion
5. The High Councils of the Church
5a. The “several quorums.”
The revelation defines the basic administrative forms and duties of the Seventy. They are to be missionaries to the gentiles (v25), act under the direction of the Q12 (v34), be first responders to missionary needs (v38), the Seventy are also called to the Jews, eventually (v97) and function as traveling ministers rather than having a fixed congregational jurisdiction.
The revelation defines the internal structure of the Seventy as given by an otherwise unknown vision(v93):
1. The quorum of the Seventy is supervised by seven presidents, who are selected from the Seventy.(v93)
2. The “seventh president” supervises or presides over the other six presidents.(v94)
3. The seven presidents may select other seventy besides the “first seventy” up to 7 additional groups of Seventy.(vs95-96)
4. The presidents belong to the first Seventy.(v95)
Symmetry might suggest that each of the seven presidents would direct one of the 7 quorums, but that strategy has never been employed (that wouldn’t work now anyway – there are 8 quorums).
After the initial announcement of the Seventy on February 28, 1835, presumably based on the vision mentioned above, the seven presidents were eventually designated (Joseph Young and Sylvester Smith were the first to be so ordained [set apart]). The seven presidents:
Hazen Aldrich (1835-1837)
Joseph Young (1835-1881)
Levi W. Hancock (1835-1882)
Leonard Rich (1835-1837)
Zebedee Coltrin (1835-1837)
Lyman R. Sherman (1835-1837)
Sylvester Smith (1835-1837)
The relative position of the Seventy among the other authorities was not well defined, despite the revelation on the subject in April 1835. Lots of competing interests were in place already like the bishops, the high councils and of course the presidency of the high priesthood. Initially the 12 were barred from interfering with stakes and the same obviously applied to the Seventy. D&C 107 marked a change in view with regard to priesthood hierarchy and the Seventy seem to be classed (vs89-90) among the elders with special assignment. The Twelve and Seventy are set apart from other officers by the requirement to “travel.” The revelation suggests that other officers might exist with just as much responsibility in the hierarchy but without the travel requirement.(v98) In fact travel requirements might be adjusted by policy statements. In Nauvoo for instance, the “standing ministers” (elders and high priests) were required to travel.
Three seventies quorums existed by 1840. They were directed by the seven presidents belonging to the first quorum. After Joseph Smith’s death in June 1844, the practice of having the seven presidents of the first quorum direct all the quorums was abandoned. In the October 1844 conference, twelve seventies quorums were organized, each with their own presidency of seven men. By 1846, 34 quorums existed and most missionaries sent from Nauvoo were seventies. In this massive reorganization of the Seventy, the original seven presidents were stripped of their quorum and became, at least on paper, a supervisory body with no quorum. Still general authorities in the sense that their authority over the Seventy cut across local congregation jurisdictions, they came to be known as the “First Council of Seventy.”
 It’s not clear what this refers to in the revelation. It’s broadest sense might include the practice known as “solemn assembly,” used for example in sustaining a new Church president.
 When the Church began to designate “Assistants to the Twelve” in 1941, one justification for the office was this verse.
 An nice summary of Nauvoo seventies is in William G. Hartley, “Nauvoo Stake” BYU Studies 32 (1992):57ff. Some of the speculation around this move suggests that Young didn’t want a Seventy that could exercise any sort of dissident move based on (what is now) D&C 107.