Recently, discriminative training (DT) methods have achieved tremendous progress in automatic speech recognition (ASR). In this survey article, all mainstream DT methods in speech recognition are reviewed from both theoretical and practical perspectives. From the theoretical aspect, many effective discriminative learning criteria in ASR are first introduced and then a unifying view is presented to elucidate the relationship among these popular DT criteria originally proposed from different viewpoints. Next, some key optimization methods used to optimize these criteria are summarized and their convergence properties are discussed. Moreover, as some recent advances, a novel discriminative learning framework is introduced as a general scheme to formulate discriminative training of HMMs for ASR, from which a variety of new DT methods can be developed. In addition, some important implementation issues regarding how to conduct DT for large vocabulary ASR are also discussed from a more pract...