Abstract : The extraction of signals of interest from electrocardiogram (ECG) recordings corrupted by noise and artifacts accepts a blind source separation (BSS) model. The BSS approach aims to estimate a set of underlying source signals of physiological activity from the sole observation of unknown mixtures of the sources. The statistical independence between the source signals is a physiologically plausible assumption that can be exploited to achieve the separation. The mathematical foundations, advantages and limitations of the most common BSS techniques based on source independence, namely, principal component analysis (PCA) and independent component analysis (ICA), are summarized. More recent techniques taking advantage of prior knowledge about the signal of interest or the mixing structure are also briefly surveyed. The performance of some of these methods is illustrated on real ECG data. Although our focus is on fetal ECG extraction from maternal skin potential recordings and atrial activity extraction in surface ECG recordings of atrial fibrillation, the BSS methodology can readily be extended to a variety of problems in biomedical signal processing and other domains.