Solving a source separation problem when the data are explained by a linear mixing of non-negative sources with non-negative mixing coefficients reduces to performing a non-negative factorization (NMF) of the data matrix. This chapter addresses the concept of NMF, discusses some of its geometrical aspects, presents the model indeterminacies, leading to a non-uniqueness of the solution, and summarizes some NMF algorithms. A focus will be made on the conditions ensuring the uniqueness of the NMF solution and on the numerical methods allowing to either calculate the set of admissible (feasible) solutions or to reduce this set by incorporating additional information or constraints on the source signals and the mixing coefficients. The application of NMF to real situations of chemical data processing is illustrated with some examples of spectroscopic data analysis.