We think of money as being a factual, straightforward thing. But actually it's very mysterious. I have a piece of paper before me as I write. Printed on it are some images, lots of hieroglyphics and the words "Twenty Pounds". If I wave it in front of a shopkeeper, it produces magical effects: in return for it, he gives me a newspaper and other pieces of paper and some bits of metal. But actually my £20 note is just that: a note. A piece of paper. What gives it its magical properties is, Professor Castronova explains, "a social process that enshrines a good as a unique artefact called money; once enshrined, that artefact serves money's three functions, well or poorly".

What are these functions? A medium of exchange, a unit of account and a store of value. As it happens, my £20 note fulfils all three functions quite well. But so did cigarettes in prisoner-of-war camps and, in days gone by, the shell of Cypraea moneta, aka the cowrie. For most of recorded history, money took almost as many forms as there were societies, or at any rate rulers, and it's only in relatively recent times that we have converged on a relatively small number of currencies together with a very small number of super-currencies, chief among them the mighty US dollar and its enfeebled fiscal cousins, the pound sterling and the euro.

Even as this process of monetary consolidation continued, however, strange new kinds of currencies were bubbling up. Supermarket trading stamps were an early example. Others include air miles, iTunes gift vouchers, discount coupons, two-for-one deals, and the numerous (and weirdly named) tokens used by online computer gaming users, Second Lifers and the like. Many of these "currencies" had money-like properties, but we did not think of them as money.

And then bitcoin arrived and suddenly everyone got very excited, or indignant, or both. Life is too short to explain it in detail, but Wikipedia does a pretty good job. Suffice it to say that it's a virtual payment system that has no central repository and no single administrator, characteristics that have led the US Treasury to call it "a decentralised virtual currency". Because bitcoins can be transferred directly from one person to another, they are sometimes described as digital cash. And because the process by which bitcoins are "mined" involves computers carrying out complex cryptographical computations, it is often called a cryptocurrency.

Bitcoin divides the world into two camps: one (the majority) thinks that it must be some kind of scam; the other (comprised mostly of geeks and venture capitalists) thinks that it's the most interesting thing since, well, sliced bread. What excites the latter is bitcoin's formidable utility as a medium for online trading.

One of the things that is holding back the net from realising its full economic potential is the high cost of conventional online payment systems, which mostly involve credit cards and high processing charges. This means that micro-payments of, say, 1p or less are impractical, and so lots of large-scale transactions and the new business models they would enable are effectively barred. Cryptocurrencies could change all that and enable the net to launch new waves of innovation and economic disruption.

Castronova doesn't dwell unduly on bitcoin, not because he doesn't regard it as significant but because for him it's really just the canary in the mine. In that sense, it plays the role that Napster did in the online music business: a harbinger of the revolution to come.

There have been lots of cryptocurrencies before bitcoins, and there are innumerable more in the pipeline – for two reasons: strangely, there appears to be no legal framework that prevents the creation of private currencies, and the digital technology to generate them is now abundantly available to all.

These are the wildcat currencies of Castronova's title. What makes his book valuable is that it's the first sustained effort to think through the implications of a world awash with such currencies. Predictably (for this is technology), it's a story of upsides and downsides.

On the plus side, cryptocurrencies seem to be pretty good as mediums of exchange: they could certainly reduce the friction in online transactions (just ask any of the traders who currently accept bitcoins) and provide much more flexibility for financing projects. They could also be a tool not just for corporations and entrepreneurs but also for state agencies. As units of account, they may be OK, but as stores of value they seem pretty questionable.

Most current discussion of the downsides of virtual currencies focuses on one aspect of them – that they are basically just tools for money-laundering. This is akin to saying the internet is just a tool for pornographers and should therefore be outlawed.

Bitcoin is useful because it is the first tangible realisation of an abstract idea – the use of cryptography to create digital currencies – to have caught the public imagination. But, Castronova argues, it's really just the beginning of a journey and we need to be thinking about where that journey will take us. He thinks that the proliferation of such currencies is a racing certainty, that the prime users/creators of them are likely to be corporations, and that the resulting proliferation will take us into uncharted territory.

The second half of his book is devoted to mapping that territory. It's about trying to imagine what a world in which there will be thousands, perhaps millions of specialised currencies would be like. The most troubling implication is that many of the (imperfect) mechanisms we have evolved for running an economy would be dissolved or undermined.

If corporations start to create currencies that exist only for days (or even minutes) in order to conduct internal transactions, for example, how will we be able to audit and monitor what's going on?

"What," Castronova asks, "if the government's ability to intervene in the economy is outpaced by the ability of organisations, even large ones, to conduct transactions invisibly?" How would investors (and pension funds) value companies? What would happen to tax revenues? Could wildcat currencies start off a spiral of state decline?

Virtual currencies are just the latest example of the challenges that digital technology is throwing up. Previous experience leads us to view the emerging possibilities as unnatural or even unthinkable. And so it is here: we've been so conditioned by our experience of "money" as something that is the inalienable province of governments and central banks that we cannot take seriously the new kinds of currency that computing can produce. I'm willing to wager my £20 note that we will live to regret our obtuseness.