I'm not sure exactly what you mean, and the uncertainty is important. By "currency", do you mean physical representations of money, such as Federal Reserve Notes or 5-pound notes? (This would seem to rule out bitcoins, which you have specifically mentioned.) Or are you talking about money in general?
In the first case, the results would be traumatic, and in some cases disastrous, but possibly not catastrophic on the larger scales. The bulk of the US economy, for instance, runs on credit rather than cash. Credit cards and debit cards, direct deposit and direct debit would still work. However, any cash transactions would obviously come to a screeching halt until such time as the US Mint could print up replacement currency, and distribute it. Which is the problem. With no way to tell who had how much cash just before the Disappearance, that distribution would be a political nightmare. In the meantime, barter would hardly take up the slack, and IOUs would only find limited use, particularly in low-income areas. There are various reasons, ranging from low values of social trust to the problems that normally cash-dependent businesses would not be able to function in the absence of cash, so local workers (who need the cash to spend on food and such) would lose their jobs as the businesses folded.
In other parts of the world, where cash is king, the results would be disaster. At the bottom of the economic ladder, subsistence farmers would be largely untouched. In the short term, they grow their own food and, if the seasons are right, won't starve immediately. The large concentrations of urban poor, though, will starve unless the local governments step up and organize distribution, and on the basis of disaster response history it does not seem likely that all of them will do so effectively. And I doubt that they'll go quietly.
This is all very bad, but it gets much worse if money (in the general sense) disappears. All credit and debit cards lose function, and all bank accounts evaporate. Not only does money include credit, it includes debt. If it all disappears, among other things this eliminates the status of all mortgages and loans. For an enormous fraction of the economy, title to real assets becomes impossible determine.
All economies above the level of barter work, to some degree, on trust. That is, if you give me money in exchange for a good or service, I'll only take it if I trust that I can find someone else who shares my opinion of what the money is worth. This includes a certain level of expectation that, if you've cheated me (by giving me counterfeit bills, for instance) that you'll end up in trouble with the Law, or that I'll be able to find you and take it out of your hide. If all the money has disappeared, replacing it would be a ticklish prospect - for instance, the temptation to start printing counterfeit bills would be enormous, and developing trust in total strangers is not an easy process.