The world of central banking is quickly turning back-to-front, inside-out and upside-down. 

Japan, the eurozone, Sweden, and Switzerland all have interest rates now that are less than zero. It's just not normal, at least in recent history, but the counterintuitive policy has helped the global economy, according to Christine Lagarde, the head of the International Monetary Fund.

Despite the oxymoronic-sounding term, the way negative rates work is fairly simple: Central banks assess a percentage charge on reserves they hold overnight for financial institutions. This gives the institutions a choice between paying to keep money in reserve or lending more cash to customers, on which they earn a return. That typically prompts them to extend more credit, which gives consumers and businesses more spending power, leading to economic growth.

So far, banks have been reluctant to pass the negative rates on to customers, with a few charging business accounts but leaving consumer funds untouched.

"The idea of negative interest rates strikes many people as odd," former Fed chairman Ben Bernanke wrote in a March blog for the Brookings Institution. "Economists are less put off by it, perhaps because they are used to dealing with 'real,' or inflation-adjusted interest rates, which are often negative. Since the real interest rate is the sticker-price, or nominal, interest rate minus inflation, it's negative whenever inflation exceeds the nominal rate."

In the U.S., real interest rates have been negative in the late 1970s, the early 2000s and for about five years after the 2008 financial crisis, Bernanke said.

While both he and his successor, Fed Chair Janet Yellen, have downplayed the likelihood that the U.S. would use negative rates, investors remain concerned because rates were cut to nearly zero during the financial crisis and nearly eight years later, they have climbed only 25 basis points, to a range of 0.25% to 0.5%.

"The anxiety about negative interest rates seen recently in the media and in markets seems to me to be overdone," Bernanke wrote. "Logically, when short-term rates have been cut to zero, modestly negative rates seem a natural continuation."

Ultimately, there are several economic scenarios in which such a strategy make sense, economists argue, and some nuanced ways it can pay off.

--When you want a weaker currency:  Negative rates can help push down the value of the currency, says Joe Brusuelas, chief economist at professional services company RSM: Who'd want to send cash to a country where your money starts losing nominal value the moment you put it in the bank?

That state of affairs may not be great for consumers shopping overseas, but it's beneficial to manufacturers like United Technologies (UTX - Get Report) whose foreign customers can buy their goods more cheaply. That typically drives up exports, increases production and can boost hiring.

Switzerland has tried the strategy and so has Japan, but it's not clear that it had a dramatic effect. That said, it is possible that both the Yen and Swiss franc could have rallied even further had it not been for sub-zero rates. 

-- When the government is dysfunctional: "Smart fiscal policy has left the building," says Constance Hunter, chief economist at professional services firm KPMG. "I am hearing more and more economists, from across the political spectrum, speak of the need for some fiscal policy action; central banks cannot do all of the heavy lifting."

"Fiscal policy action" is frequently used a euphemism for boosting government spending to create jobs and buoy the economy, a strategy President Franklin D. Roosevelt employed in the U.S. with some success after the Great Depression of the 1930s.

Such moves typically require legislative cooperation, however, and sometimes countries get stuck with political parties unable to work together. That seems to have been what's happened in the eurozone, where there is little interest in the various governments spending more to lift economic activity. Hence, the pressure is now on the European Central Bank to do whatever it can on its own to boost the economy.

-- When there's deflation: When prices are falling, negative interest rates can provide economic benefits with minimal impact on consumers. 

How's that work? If the decline in prices is steeper than the negative rate of interest, then your money will still have more spending power after 12 months. For example, if prices fall 10%, but you have a negative interest rate of 5% at the bank, your money still buys you more, even though the nominal value of the account is smaller.

Although deflation hasn't hit the U.S., it's well-established in Switzerland, David Ranson, director of research at consulting firm HCWE Worldwide Economics, writes in a recent report, so "negative rates are natural and to be welcomed."

Read More: See TheStreet's full 'Below Zero' package here.