In the comments section of my post on Adam Smith and the Ayr Bank, frequent commenter John S. brought up the real bills doctrine. The phrase real bills doctrine gets thrown around a lot on the internet. To muddy the waters, there are several versions of the doctrine. In this post I hope to dehomogenize the various versions in order to add some clarity.
1. Lloyd Mints's version
We may as well start with Lloyd Mints's version, since he coined the phrase real bills doctrine back in 1945 on his way to denouncing the doctrine. Mints taught at the University of Chicago and mentored Milton Friedman.  Here is Mints:
The real-bills doctrine runs to the effect that restriction of bank earning assets to real bills of exchange will automatically limit, in the most desirable manner, the quantity of bank liabilities; it will cause them to vary in quantity in accordance with the "needs of business"; and it will mean that the bank's assets will be of such a nature that they can be turned into cash on a short notice and thus place the bank in the position to meet unlooked-for calls for cash. - A History of Banking TheoryMints's RBD states that so long as only real-bills (short term liquid debt instruments created by merchants to finance inventory) are discounted by the banking system, an excess amount of notes can never be issued. When businesses require cash, they'll simply discount bills at a bank, and when that cash is no longer required, they'll pay back their borrowing. Even in a world *without* note convertibility into specie (a "fiat standard") the real bills stipulation alone is sufficient to keep the price level anchored.
Mints rightly declared that this version of the RBD was "completely wrong". After all, a central bank not constrained by convertibility might discount only real bills, yet by discounting at an unreal price, it would alter the purchasing power of the notes it issues and create either runaway inflation or deflation). The price level was indeterminate in Mints's RBD-world.
Mints singled out Adam Smith for being "the first thoroughgoing exponent of the real-bills doctrine". For the next forty years, Smith's reputation as a monetary theorist would be tarnished. 
2. Adam Smith's version
Though tarred and vilified, poor Adam Smith never actually conformed to the real bills doctrine as described by Mints. This has been pointed out by David Laidler in his 1981 paper Adam Smith as a Monetary Economist, one of the first efforts to rehabilitate Smith's reputation as a monetary theorist.
Smith lived in an era in which paper money was fully convertible into a fixed amount of gold. Mints's description of the RBD, on the other hand, applies to a fiat world. For Smith, the gold convertibility clause was sufficient to ensure that the economy needn't endure an excess amount of notes. After all, should banks as a whole issue more than was desired, the public would return the notes en masse for specie. This is the so-called reflux process.
That being said, Smith did mention real bills several times in the Wealth of Nations. He famously advises banks that they should only discount "real bills of exchange drawn by a real creditor upon a real debtor." (I go into some detail in my last post on the personal and historical reasons that may have motivated Smith to advocate this position).
Why limit discounts to real bills? When the banking system issues excess paper currency, gold convertibility ensures that this excess will soon reflux back to issuer. A bank that holds long term loans and bonds issued by speculators will be insufficiently prepared to meet the demands of reflux since liquidating such debts might take time. A bank that holds short term bills issued by credit-worthy merchants will be better equipped to meet redemption demands, and less likely to meet the same demise as that experienced by the Ayr Bank, a bank run that Smith personally witnessed.
Thus Smith's admonishment to only discount real bills wasn't a mechanism for anchoring the economy's price level—gold convertibility served this purpose. Smith's real bills stipulation was just good advice for individual banks: stay liquid and don't take on too much credit and term risk. This distinction has been aptly described by David Glasner in his paper the Real Bills Doctrine in the Light of the Law of Reflux, and for his part Laidler notes that "as advice to an individual bank, it's probably pretty sound, as a principle of
monetary policy under commodity convertibility it is relatively harmless..." [link]
3. The Bank Directors' version
Why did Mint's cast Adam Smith as his first thorough-going exponent of the RBD?
In 1797, some seven years after Smith had died, Britain went off the gold standard. (See this post for details). The pound soon began to trade at a discount to its pre-1797 gold value. In other words, the pound was capable of purchasing less gold. The Directors of the Bank of England found themselves accused of creating inflation, notably by the members of the 1810 Bullion Committee. One of the apologizers for the Directors, Charles Bosanquet, a pamphleteer, wrote a famous rebuttal in 1810 that insisted that by limiting discounts to "solid paper for real transactions," the Bank could not have contributed to a deprecation of the pound. According to Bosanquet, several factors outside of the Bank's control had caused the deprecation.
To help buttress his point, Bosanquet invoked the name of Adam Smith. Wrote Bosanquet: "The axiom, or rule of conduct, on which the Committee has been pleased to heap contempt and ridicule, respecting which they have declared that the doctrine is fallacious, and leads to dangerous results, was promulgated by, and is founded on, the authority of Dr. Adam Smith."
Bosanquet's appropriation of Smith's name was inappropriate since Smith implicitly assumed gold convertibility. But the damage had been done. From then on, economic historians like Mints would automatically associate Smith's name with the arguments of the Directors.
The Directors' RBD is very much a manifestation of Lloyd Mints's RBD, which we already know was a poor guide for monetary policy. Years later, Walter Bagehot would write that when the Directors were examined by the Bullion Committee in 1810, "they gave answers that have become almost classical by their nonsense". If anyone deserved to be castigated as the first thoroughgoing exponents of Mints's real bills doctrine, it was the Directors and not Smith.
4. Antal Fekete's version
If you've spent some time wading through the online monetary economics community, you'll have run into Antal Fekete's real bills doctrine. This is an attempt to apply a warmed over version of Adam Smith's RBD mixed in with some Austrian free market economics.
The use of bills of exchange began to diminish in the late 1800s and today they are a relatively unimportant financial instrument, having been replaced in bank portfolios by commercial paper, bonds, mortgages, and other types of debt. Fekete tries to draw a number of broad based conclusions from this trend. The crowding out of real bills by non-real bills (longer term finance bills and government issued treasury bills), for instance, is seen by Fekete as the reason for the Great Depression and the creation of the modern Welfare state:
When real bills were replaced by non-self-liquidating finance bills, payment of wages has become haphazard. Employment was made touch-and go, hiring, ‘hand-to-mouth’. This threatened with unemployment on a massive scale, unless governments were willing to assume responsibility for paying wages. [Link]Conversely, rehabilitating the real-bills system would end chronic unemployment and reduce the size of government. I only have a passing knowledge of Fekete's thinking — it really doesn't do much for me —so hopefully someone in the comments section can pick up the slack.
5. Mike Sproul's version
Of the modern reincarnations of the RBD, I'm far more familiar with Mike Sproul's version.
Mike's version is an application of modern finance to monetary economics. The price of a financial asset is determined by the discounted value of the expected flows of cash thrown off by underlying capital. Alcoa's stock price, for instance, will equal the sum of discounted earnings that Alcoa's machinery and employees are expected to generate. Transferring this idea to the monetary landscape, Mike says that value of modern central bank liabilities should be determined by the earnings power of the assets held by that central bank.
Like the other versions of the RBD, Mike's version shares a preoccupation with the asset side of a bank's balance sheet. But that ends their similarity. For instance, Mike doesn't have a fetish for actual real bills. I doubt he'd agree with the Directors that so long as they only discounted short-term mercantile bills of exchange, they'd never cause a decline in the value of the pound.
That's why I prefer to call Mike's RBD the backing theory. It's a very different beast from the RBDs of Mints, Smith, Fekete, and the Bank Directors, and to share the same name only adds to the confusion.
So there you have it. If you're going to have an argument over the RBD, make sure you know which one you're arguing about!
1. Fischer Black received this letter from Milton Friedman on August 6, 1971: "With respect to your so-called passive monetary policy, here you are simply falling into a fallacy that has persisted for hundreds of years. I recommend to you Lloyd Mints' book on The History of Banking Theories for an analysis of the real bills doctrine which is the ancient form of the fallacy you express. Do let me urge you to reconsider your analysis and not let yourself get misled by a slick argument, even if it is your own. " Ouch. Play nicely, Milt. I get this via Perry Mehrling's book on Fischer Black.
2. Here's a video of Lloyd Mints in 1988 upon his 100th birthday.