Abstract: Source separation is a difficult problem for which many algorithms have been proposed. In this article, we define oracle estimators which compute the best performance achievable by different classes of algorithms on a given mixture, in a theoretical evaluation framework where the reference sources are available. We describe explicit oracle estimators for three particular classes of algorithms: multichannel time-invariant filtering, single-channel time-frequency masking and multichannel time-frequency masking. We evaluate their performance on various audio mixtures and study their robustness. We draw several conclusions for their three typical applications, namely providing performance bounds for existing and future blind algorithms, selecting the best class of algorithms for a given mixture and assessing the separation difficulty. In particular, we show that it is worth developing blind time-frequency masking algorithms relaxing the common assumption of a single active source per time-frequency point.