Non-negative compositional models are of great importance in the application of artificial intelligence, data mining and intelligent information processing research. They have gradually become one of the most representative and frequently used models of acoustic source separation in recent years. The embedded additive combination of non-negative components matches well with the characteristic of human perception. Techniques that make use of non-negative compositional models have been increasingly popular in acoustic source separation. Starting from the most basic non -negative compositional model, which is termed as non-negative matrix factorization (NMF), we firstly review the principles of non-negative compositional model, including the basic problem to be solved, the measurement of objective function and some typical methods to solve related problems. Based on these principles, we systematically discuss the variety extensions of NMF designed for particular applications in acoustic source separation. Finally, some open problems are presented and discussed. 