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Discriminative training techniques have been shown to consistently outperform the maximum likelihood (ML) paradigm for acoustic model training in automatic speech recognition (ASR). Consequently, today's discriminative training methods are fundamental components of state-of-the-art systems and are a major line of research in speech recognition. This article gives a comprehensive overview of discriminative training methods for acoustic model training in the context of ASR. The article covers all related aspects of discriminative training for speech recognition, i.e., specific training criteria and their relation, statistical modeling, different parameter optimization approaches, efficient implementation of discriminative training, and a performance overview.