This document is a comprehensive survey of advancements in automatic dysarthric speech recognition (DSR) utilizing machine learning (ML) and deep learning (DL) methodologies. It emphasizes the impact of dysarthric speech, caused by various neurological disorders, on communication and explores the methodologies, databases, evaluation metrics, and findings of existing research in DSR, revealing that DL techniques generally outperform traditional ML methods. The paper identifies gaps in current research and suggests future directions for enhancing DSR effectiveness.