Abstract : The present chapter addresses the problem of channel equalization and source separation in digital communications. Semi-blind techniques incorporate training symbols into blind criteria and arise as a judicious compromise benefiting from the advantages of supervised and blind techniques. Algebraic (i.e., closed-form) solutions can provide perfect equalization in the absence of noise, and are shown to be connected to matrix and tensor algebra problems. Iterative semi-blind equalizers are useful in the presence of noise, and can be efficiently implemented by an optimal step-size gradient-based search. The optimal combination of the training and blind criteria is also addressed.