  The review introduces the history of cryptocurrencies, offering a description
of the blockchain technology behind them. Differences between cryptocurrencies
and the exchanges on which they are traded have been shown. The central part
surveys the analysis of cryptocurrency price changes on various platforms. The
statistical properties of the fluctuations in the cryptocurrency market have
been compared to the traditional markets. With the help of the latest
statistical physics methods the non-linear correlations and multiscale
characteristics of the cryptocurrency market are analyzed. In the last part the
co-evolution of the correlation structure among the 100 cryptocurrencies having
the largest capitalization is retraced. The detailed topology of cryptocurrency
network on the Binance platform from bitcoin perspective is also considered.
Finally, an interesting observation on the Covid-19 pandemic impact on the
cryptocurrency market is presented and discussed: recently we have witnessed a
"phase transition" of the cryptocurrencies from being a hedge opportunity for
the investors fleeing the traditional markets to become a part of the global
market that is substantially coupled to the traditional financial instruments
like the currencies, stocks, and commodities.
  The main contribution is an extensive demonstration that structural
self-organization in the cryptocurrency markets has caused the same to attain
complexity characteristics that are nearly indistinguishable from the Forex
market at the level of individual time-series. However, the cross-correlations
between the exchange rates on cryptocurrency platforms differ from it. The
cryptocurrency market is less synchronized and the information flows more
slowly, which results in more frequent arbitrage opportunities. The methodology
used in the review allows the latter to be detected, and lead-lag relationships
to be discovered.

Statistical Finance;Computational Engineering, Finance, and Science;Econometrics;Computation