Summarizing and expanding a bit here. Responsibility profiles for the PB have varied. In the 1970s they became more deeply connected with the Church’s youth organizations. Eventually that role was withdrawn and they now function in supervising Church business matters including real estate, commercial corporate interests, humanitarian operations, etc. though at present the Presiding Bishop sits on the Church PEC, hence he is a discussion partner in youth issues.
It’s commonly proposed (similar to what was discussed in part 3 of this post relative to D&C 68 and D&C 107) that the PB is the body that can adjudicate a disciplinary case involving a Church President (or possibly a counselor in the First Presidency – though that is less clear). This is false in the sense that it never did nor does it now exist as a revelatory paradigm. When D&C 107 was incorporated in the 1835 Doctrine and Covenants (as section 3), there was no PB, much less when the November 11, 1831 revelation was delivered. Only local bishops (twice) ever sat in judgement on a First Presidency member and revelations delivered in January 1838 (and canonized shortly after in Missouri) revoked that process and moved it to multi-local one (every stake had to hold a trial and majority rules. It was more complex than that though.) The current philosophy (Wilford Woodruff was point man here, though he followed somewhat similar claims from BY and even JS) is that God will simply cause the death of a rogue president. In reality, barring death, a rogue president — hardly a likely scenario, would find it hard to get away with much. President Kimball for example, while convinced that priesthood restriction had to go, took a considerable period before broaching the subject to other leaders. Consensus is key.
PB members have never been subject to fixed retirement schedules. While the Seventy in the general quorums are usually released from service by age 70, some members of the PB presently exceed that age by a substantial margin. The current PB consists of Harold David Burton (age 74), Richard Crockett Edgley (age 77) and Keith Brigham McMullin (age 71). [Ages approximate.]
Current Church literature declares that the Presiding Bishop has the “keys of the Aaronic Priesthood” (all ward bishops have these keys according to the most recent handbook of instructions). Ward bishops function per D&C 107 as president of a quorum, the priests quorum. Since the PB has no quorum, there is a slight terminological problem I suppose. There’s a lot more fun there, given various explanations of the word over the last thirty years. That goes beyond the scope of this stuff.
The PB has always exercised considerable authority in financial matters and bishops in general have the same charge. The interface between the PB (in this role) and other Church leaders has had its interesting moments. During Joseph Smith’s and Sidney Rigdon’s first visit to Missouri in 1831, the bishop (Partridge) was in charge of providing transport for their return trip along with other traveling companions. Partridge bought canoes for the party and Rigdon never forgave him for his cheaping out (Rigdon’s canoe capsized and he nearly drowned along with some of the others — budding dissenter Ezra Booth who was along for the ride used the incident to poke fun at Sidney and Joseph).The (central) Tithing Office in early Salt Lake City, essentially a bishop’s storehouse, was sometimes a source of friction between the PB and other Church leaders and staffers (following in the well-trodden footsteps of the Nauvoo temple committee) and the PB could be somewhat stingy in reimbursing travel according to some apostles in the early 1900s. The office has never had a clear peerage with the Seventy, though in the past members of the PB have moved into the Seventy since the latter’s reorganization in 1976 (after being released from the PB) or to the former “Assistants to the Twelve” or even the Q12 or First Presidency (e.g., Nibley).
Since the organization of general authority seventies quorums and the shrinkage in the number of general conference sessions (PB members usually spoke in general welfare sessions before those ceased) conference speech time has become a premium. It is rare for more than one member of the PB to speak in a general conference but at least one gets the nod at each conference in recent years.
PB members who spoke in a given April or October conference since 2007:
2007 April (Burton and McMullin)
2007 October (Edgley)
2008 April (Burton)
2008 October (McMullin)
2009 April (Edgley)
2009 October (Burton)
2010 April (McMullin)
2010 October (Edgley)
2011 April (Burton)
2011 October (McMullin)
So at least since October 2007 one member of the PB has spoken in General Conference. Apparently, Bishop Edgley is up to bat. The conference topics of PB members have not been restricted to welfare or other temporal issues. The first bishops were temporal ministers seen as part of the New Testament’s dictum to seek after and care for the poor, an emphasis augmented by Joseph Smith’s revisions and additions to biblical texts and early revelations. The office evolved to temporal/financial duties and a spiritual ministry — bishops keep the doors of the temple (and Church employment) and oversee the first ecclesial level of Church administration. The bishoprics gradually assumed much of the duties and responsibilities of early Melchizedek Priesthood quorums and became the exclusive first line of Church discipline. Local bishoprics were key players in the coming of correlation. That is just too much to get into here. The Presiding Bishopric actually had a less radical change spectrum and have never been associated with the title “presiding high priest.”
The Presiding Bishopric. An office born out of revelation, expanded and focused by necessity. Next time your church building floods, call me. I’ll give you their phone number. Next conference, I’m bound to do another one of these. I’ll take requests.
 The PB has always had some role in Aaronic Priesthood issues. The role seems less evident now than in the past. For example, in 1960s, Aaronic Priesthood matters in local units were to be taken directly to the PB. Present Church handbooks don’t mention the Presiding Bishopric much beyond a few financial issues. At the beginning of the 20th century, the Presiding Bishop was still a regular speaker in the general priesthood session of general conference. Minutes of these sessions show the PB addressing the training of young AP holders. In terms of recent years, you may have observed Bishop Burton on the stand at the recent general YW meeting.
 See Edward Kimball’s recent biography of President Kimball (you should read the CD version that comes with the book).
 The First Council of Seventy didn’t get much face time in general conference until the 1890s. The somewhat earlier expansion of the recorded public speaking corps had much to do with the Raid. The FCS was chronologically ahead of the PB in local Church administration by ten years or so. These days, a GA is a GA is a GA.
 Early priesthood quorums had responsibility for discipline of quorum members in terms of their ability to function as priesthood holders and even on occasion, Church membership. A return of those days would make for fun stuff. Correlation might be good for uniformity, but it removed a lot of distributed power and responsibility. Easier for upper level control though.
 One very important topic I have not explored is the relationship between the PB and the Relief Society, which was also in the business of temporal ministry. With correlation, RS assets came under the PB’s control. Another topic skirted here: Gentiles! A complex relationship existed with Utah gentiles and the PB.