The first major current of thought was Mercantilism. Its defining focus was on having a positive balance of trade, and a constant concern that the country will run out of money (gold, back then). It emphasized state control of the economy, with heavy tariffs, regulations and taxes, with the intent that the absolute monarchy rule all aspects of life.
Afterwards, classical economics took the stage, and advocated for a hands-off approach. We all know how the industrial revolution took place under its guidance. Certainly, there was a severe lack of capital to go with the labor pool, due to improved agricultural productivity freeing farmers and putting them into industrial production.
Up until this point, however, intellectuals wrote about economics as a hobby, rather than as an academic profession. Adam Smith, for example, taught ethics at a university. This showed in his description of capitalism:
We could say that other systems are about playing zero-sum (or even negative-sum) games, while capitalism is about positive-sum games. This is why often, those who became rich in questionable ways are resented for their wealth; but prominent industrialists, from Henry Ford to Steve Jobs are regarded as heroes.
During the Industrial Revolution, however, some economists got "physics envy". They jealously watched the incomprehensible mathematics of the physicists and engineers. They mistook the accounting for the substance, and thought that science was made by the maths.
Thus they started creating partial differential equations of their own. Inspired by the gas laws, perhaps, they created the theory of general equilibrium. The problem was, however, that not everything was easy to quantify. Prices and quantities, wages, interest rates were easy to handle; taxes and regulations not so.
But they were only willing to use one tool, and thus anything they couldn't easily fit to the tool, they discarded. They proved that a stable equilibrium must always exist, and wrote how government intervention—price limits and such—would distort the market. And they got tenure.
Thus they willingly limited their studies to prices, interest rates and money. Everything else fell by the wayside. But, the problem was, their model didn't have anything left that could cause large recessions.
Enter the Smoot-Hawley tariff act. Fueled by protectionism, it was passed into law in 1930, after bumbling through the American legislation during the previous year. Immediately, its main trading partners responded in kind, and a global tariff war broke out. Between 1929 and 1933, US imports fell by 66% and exports by 61%.
Then, as the tariffs choked international trade, and government revenue started to fall, states increased taxes. They were very beholden to the idea of balanced budgets, because the classical economists models predicted (correctly) that a state that runs significant deficits indefinitely will eventually default under the weight of the obligations.
I need not elaborate that stiff tariffs and taxes are bad for all economies involved. However, the economists of the era (and today) did not include tariffs and taxes in their mathematical models with much attention to detail. Thus when they saw a general meltdown of the economy, they looked for price controls (there weren't any), interest rate manipulation (none) or problems with the money.
And here they split into multiple camps, not knowing what to do with the situation. The more ardent classicalists didn't see any problems, and thus just shrugged, saying that a new equilibrium will eventually form.
Some more mercantilism-oriented said that, apparently, the factories (aggregate supply) were fine, but aggregate demand must have fallen. Prices and quantities alike dropped, this is what must have happened. Thus the government should spend a lot of money, put it into the hands of the people, so that they would go and consume. Also, the money should be inflated away, so that people would not hoard it, instead go and consume. Further, they insisted that interest rates should decline—although they were already as low as possible.
They apparently ignored the fact that savings are the other side of investment, and it is perhaps unwise to hinder investment. More tellingly, they couldn't explain where the sudden decline in demand came from! Yet although they didn't know what caused the problem, they were quite certain that spending and devaluation would cure it.
Perhaps the clearest case was when John Maynard Keynes more or less boasted, that the government should pay people to dig ditches and then pay them to fill them in. When saner heads pointed out that in the long run, no country on Earth became wealthy by digging and filling ditches (i.e. wasting a lot of time and effort, rather than putting it toward productive investment), and that in the long run, no society could devalue its way to prosperity, he answered: in the long run, we are all dead.
Now Keynes is dead and we are living in the long run. However, spending lots of money with no responsibility for spending it wisely, and devaluing the debt of the government was exactly what politicians wanted to hear. They put the recommendations into practice enthusiastically.
A third group found no problem with prices and interest rates either, hence the answer must lie with money, right? They fixated on the observation that the overall quantity of debts decreased significantly. Of course it did, who wants to borrow—or lend, for that matter—in the middle of an economic meltdown? Then they mixed up this credit volume contraction with an increasing value of money, a.k.a. deflation. They are the monetarists.
Ever since then, politicians are happy to listen to Keynesian economists. The distinctly mercantilist idea, that capitalism sometimes just blows up all by itself and needs constant and extensive state management is naturally appealing. The recommended cure, reckless spending on anything that catches their fancy, even more so.
This causes no end to economic woes. During the Bretton Woods system (1945-71), the dollar was officially convertible to gold (at $35 an ounce), and other currencies were fixed to the dollar. However, the American politicians and central bankers couldn't quite restrain themselves, and tried to have another monetary policy at the same time.
Now, I've explained how a central bank can keep its currency arbitrarily close to its target exchange rate, by acting as a currency board. They didn't, because they also tried to keep interest rates artificially low. Turns out, the two are not compatible with each other, and the value of the dollar kept being lower than it should have been.
Now, the Federal Reseve (the US central bank) started the Bretton Woods era with more than half of all gold on Earth in its vaults. Quite an incredible feat, and absolutely impossible to screw up, right? Yes, if you know what you are doing. The Bank of England was the center of a gold standard with less than 5% of all gold, and they kept it for about two centuries, albeit with a few suspensions during wars.
But the economists of the Bretton Woods era didn't know what they were doing, apparently. Because they kept issuing too many dollars due to their low interest rates (trying to spur the economy into even faster growth), the surplus dollars were kept being given back and exchanged for gold. But then—rather than sitting on them as they should have—they kept reissuing them. Thus gold steadily trickled out of the vaults.
In effect, the Fed tried to inflate the gold market into parity with the weakening dollar, rather than shoring up the currency. However, they eventually ran out of gold with which to do it, and in 1971 officially suspended convertibility.
In the US, this was followed by a decade of massive inflation. They tried to devalue their way into prosperity, just as the Keynesians told them. It didn't work. Then they got fed up with the rampant inflation, and—looking at the Phillips curve—concluded that the only way to do that is to have a significant recession. If that is the way to have low inflation (rather than—you know—managing the money correctly via a currency board), then so be it, they said, and had several years of depression.
The crisis was primarily a financial one, about various bank-like organizations going bankrupt, or nearly so. In some respects, the domino effect that happened among highly levered balance sheets was an opposite of a short squeeze. When one entity went bankrupt (or approached the threshold), it had to sell a large fraction of its assets, pushing their price down. This, by mark-to-market accounting, hurt the assets of all the other banks, which came closer to bankruptcy in turn.
One way to halt the crisis (and eventually make a profit in the process) is to buy a lot of new equity in the teetering banks. After the crisis is over, and asset prices rebound, that equity can be sold at a profit. And where to get the money from? Add a big IOU to the bank's assets. The state would have been able to do this without any difficulty.
Instead we had several "bail-in"s. The essence of this is to use a single failed bank as a dumpster, and sell any unwanted assets to it, often even below their market value. And it would be the depositors who would eat the losses.
To anyone knowing how banks are supposed to work, this is daylight robbery. Retail depositors are the most senior creditors of the bank. Even if a bank goes bankrupt, i.e. its share capital is zero (let's be optimistic instead—it has infinite leverage!), there are more junior creditors than the retail depositors. For example, corporate clients. Only if their liabilities are unfunded, does Average Joe start to take a loss.
A second problem is the impotency of monetary policy. Several rounds of quantitative easing, yet apparently little result. Another case of the "official" economists not understanding their field.
This is largely due to them being beholden to the quantity theory of money. Thus they assumed that if the liabilities of the central bank increase, the value of the currency would fall. The fact that several rounds of QE were held, yet there is still an ongoing discussion about how to avoid deflation, shows the magnitude of the failure.
"Insanity is doing the same thing over and over, expecting a different result." This is the really troubling part—that after the failure of one round of QE, the decision was not to slow down and find out what's actually going on, but double down and repeat the action that was already known to be ineffective.
The explanation for the failure lies in the fact that money isn't an unfunded liability like gold or bitcoin. In fact it derives most of its value from its backing, and QE did nothing to decrease that. It only decreased the already thin liquidity premium on money, and perhaps lengthened the time-to-redemption.
Thus the best solutions are the ones that could leave the central bank's assets unchanged while decreasing its leverage. One way to do this is to peg to something else at the current market rate with a currency board and start shifting the peg. Another is to add a fee on redeeming liabilities, or to limit the quantity that can be redeemed per day. A very radical option is to convert the debt into equity, and start running a loss. This would mean that the National Bank would become a National MMMF trying to break the buck on purpose. Of course, when it would run a surplus, it would give that over to the treasury.