Speech is the primary means through which human beings interact. Speech has become a way for Man Machine Interaction (MMI). The Speech Recognition (SR) systems have been widely used in smart phones to initiate searches or to type certain text messages, and in control devices to perform switch on or off functions etc. This system comprises three blocks: Pre-processing, Feature Extraction and Classification. The input speech signal is pre-processed to remove the noise and to convert it into a digital form for feature extraction. The feature extraction is a significant process during SR systems design because the features extracted form the basis for accurate recognition of the speech. Only a few features of this signal may be selected for classification purposes. For final recognition of the spoken word or the input signal, various optimization algorithms as classifiers are used. This paper presents an extensive literature review on SR Systems. The authors have attempted to do a brief survey to identify the progress in this field. The survey provides the reader with well-known methods used by previous researchers. It also compares the performance metrics for two ASR techniques developed by the authors. The first technique uses Artificial Neural Network with Back Propagation while the second uses Fuzzy based Discrete Wavelet Transform. It was found that the fuzzy based DWT system provided better results in terms of the performance metrics like accuracy, sensitivity, specificity and word error rate. The paper concludes by providing the reader with a direction of future scope in this research area.