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This study is an integrated survey of GARCH methodologies applications on 67 empirical papers that focus on cryptocurrencies. More sophisticated GARCH models are found to better explain the fluctuations in the volatility of cryptocurrencies. The main characteristics and the optimal approaches for modeling returns and volatility of cryptocurrencies are under scrutiny. Moreover, emphasis is placed on interconnectedness and hedging and/or diversifying abilities, measurement of profit-making and risk, efficiency and herding behavior. This leads to fruitful results and sheds light on a broad spectrum of aspects. In-depth analysis is provided of the speculative character of digital currencies and the possibility of improvement of the risk–return trade-off in investors’ portfolios. Overall, it is found that the inclusion of Bitcoin in portfolios with conventional assets could significantly improve the risk–return trade-off of investors’ decisions. Results on whether Bitcoin resembles gold are split. The same is true about whether Bitcoins volatility presents larger reactions to positive or negative shocks. Cryptocurrency markets are found not to be efficient. This study provides a roadmap for researchers and investors as well as authorities.