This paper surveys the academic literature concerning the formation of pricing bubbles in digital currency markets. Studies indicate that several bubble phases have taken place in Bitcoin prices, mostly during the years 2013 and 2017. Other digital currencies of primary importance, such as Ethereum and Litecoin, also exhibit several bubble phases. The Augmented Dickey Fuller (ADF) as well as the Log-Periodic Power Law (LPPL) methodology are the most frequently employed techniques for bubble detection and measurement. Based on much academic research, Bitcoin appears to have been in a bubble-phase since June 2015, while Ethereum, NEM, Stellar, Ripple, Litecoin and Dash have been denoted as possessing bubble-like characteristics since September 2015. However, this latter group possess little academic evidence supporting the presence of bubbles since early 2018. An overall perspective is provided based on a robust bibliography based on large deviations of market quotes from fundamental values that can serve as a guide to policymakers, academics and investors.