Automatic dysarthric speech recognition (DSR) is very crucial for many human computer interaction systems that enables the human to interact with machine in natural way. The objective of this paper is to analyze the literature survey of various Machine learning (ML) and deep learning (DL) based dysarthric speech recognition systems (DSR). This article presents a comprehensive survey of the recent advances in the automatic Dysarthric Speech Recognition (DSR) using machine learning and deep learning paradigms. It focuses on the methodology, database, evaluation metrics and major findings from the study of previous approaches.The proposed survey presents the various challenges related with DSR such as individual variability, limited training data, contextual understanding, articulation variability, vocal quality changes, and speaking rate variations.From the literature survey it provides the gaps between exiting work and previous work on DSR and provides the future direction for improvement of DSR.