Reversing the usual direction of simulation, the QRST says that noiseless quantum channels can efficiently simulate noisy ones, in the presence of shared entanglement between sender and receiver. The theorem is now known to hold for some channels on all sources, and for all channels on known or unknown tensor product sources, IID or non-IID. Joint work with Igor Devetak, Aram Harrow, Peter Shor, and Andreas Winter.