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This paper classifies and reviews the available algorithms to blind signal separation (BSS) problem. Based on the separation criteria, we broadly divide all the reviewed algorithms into four categories, namely: classical adaptive, higher-order statistics based, information theory based algorithms and others. For algorithms which might fall into more than one category, categorizing is made according to their main features. Most of the algorithms reviewed in this paper are benchmarks in BSS area. Many BSS algorithms use neural networks to perform the learning rules, probably because neural networks are powerful in nonlinear mapping and learning ability.