Speech disorders are the conditions in people which affect their ability to speak properly i.e., different from normal fluency in speaking. These speech issues are usually generated due to a variety of neurological issues. The proper and correct analysis of these disorders is always required for the recommendation of their treatment. The analysis of speech signals may provide a deep insight into the type of speech-related issues. In this paper, a thorough analysis is performed for speech signals-based speech disorder analysis. Various types of speech disorders are discussed here, along with their treatments and diagnosis methods. Furthermore, various steps involved in the speech signals-based analysis are thoroughly examined. Various traditional models as well as novel deep learning models are further discussed along with their applicability in detecting different types of disorders. Speech disorders such as Dysarthria, stuttering, voice disorders, etc. are considered here for analysis.