Rough stochastic volatility models provide a powerful modelling framework for equity markets, capturing important stylized facts on realized variance time series as well as implied volatility surfaces. However, the price and variance processes in those models are difficult to handle theoretically and numerically, since they are no semimartingales and lack the Markov property. In this work we show that popular rough volatility models can be approximated by low-factor Markov processes with very high accuracy. Additionally, those Markovian approximations can be chosen such that the resulting Markov processes can be efficiently simulated by standard weak approximation schemes. As an example, we provide highly accurate simulation algorithms for the rough Heston model based on only two-factor Markovian approximations of the variance process. (Joint work with Simon Breneis.)