We consider the problem of convolutive blind source separation (BSS). This is usually tackled through either multichannel blind deconvolution (MCBD) or using frequency-domain independent component analysis (FD-ICA). Here, instead of using a fixed time or frequency basis to solve the convolutive blind source separation problem we propose learning an adaptive spatial–temporal transform directly from the speech mixture. Most of the learnt space–time basis vectors exhibit properties suggesting that they represent the components of individual sources as they are observed at the microphones. Source separation can then be performed by projection onto the appropriate group of basis vectors.We go on to show that both MCBD and FD-ICA techniques can be considered as particular forms of this general separation method with certain constraints. While our space–time approach involves considerable additional computation it is also enlightening as to the nature of the problem and has the potential for performance benefits in terms of separation and de-noising.