This paper introduces new methods for analysing the extreme and erratic behaviour of time series to evaluate the impact of COVID-19 on cryptocurrency market dynamics. Across 51 cryptocurrencies, we examine extreme behaviour through a study of distribution extremities, and erratic behaviour through structural breaks. First, we analyse the structure of the market as a whole and observe a reduction in self-similarity as a result of COVID-19, particularly with respect to structural breaks in variance. Second, we compare and contrast these two behaviours, and identify individual anomalous cryptocurrencies. Tether (USDT) and TrueUSD (TUSD) are consistent outliers with respect to their returns, while Holo (HOT), NEXO (NEXO), Maker (MKR) and NEM (XEM) are frequently observed as anomalous with respect to both behaviours and time. Even among a market known as consistently volatile, this identifies individual cryptocurrencies that behave most irregularly in their extreme and erratic behaviour and shows these were more affected during the COVID-19 market crisis. © 2020 Elsevier B.V. All rights reserved.