[Cryptography] Digital currencies

[John Levine]

>How far advanced are the developments in digital currencies?

Somewhat.

>Would they ever be able to replace the classical currencies?

No.  (That was easy.)

Digital currencies solve some interesting problems, like a
decentralized ledger (which may or may not be cheap depending on how
you allocate the costs of mining or whatever replaces it) and
conditional transactions aka smart contracts.

Real currencies have other characteristics which have little or
nothing to do with technology.  Every successful modern currency has a
central bank that manages the money supply and interest rates.
Successful payment systems generally have a way to reverse fraudulent
transactions, which requires a human authority to decide what was
fraudulent and not just buyer's remorse.

We are much more likely to see hybrid systems.  See, for example, this
article about experiments by the Bank of Canada to use a blockchain
for C$ payments among large banks:

http://www.ft.com/intl/cms/s/0/1117c780-3397-11e6-bda0-04585c31b153.html

R's,
John