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The paper presents a systematic review of acoustic modeling (AM) techniques in speech recognition (SR). Acoustic modeling establishes a relationship between acoustic information and language construct in SR. Over the past decades, researchers presented studies addressing specific concerns in AM. However, all previous research works lack a systematic and comprehensive review of acoustic modeling issues. A systematic review is introduced to understand the acoustic modeling issues in speech recognition. This paper provides an extensive and comprehensive inspection of various researches that have been performed since 1984. The extensive investigation and analysis into AM was performed by getting the relevant data from 73 research works chose after the screening process between the years from 1984 to 2020. The systematic review process was divided into different parts to investigate acoustic modeling issues. Main issues in acoustic modeling such as feature extraction techniques, acoustic modeling units, speech corpora, classification methods, different tools used, language issues applied, and evaluation parameters were investigated. This study helps the reader to understand various acoustic modeling issues with comprehensive details. The research outcomes presented in this study depict research trends and shed light on new research topics in AM. The result of this review can be used to build a better speech recognition system by choosing a suitable acoustic modeling construct in SR.