Automatic speech recognition (ASR) has recently become an important challenge when using deep learning (DL). It requires large-scale training datasets and high computational and storage resources. Moreover, DL techniques and machine learning (ML) approaches in general, hypothesize that training and testing data come from the same domain, with the same input feature space and data distribution characteristics. This assumption, however, is not applicable in some real-world artificial intelligence (AI) applications. Moreover, there are situations where gathering real data is challenging, expensive, or rarely occurring, which can not meet the data requirements of DL models. deep transfer learning (DTL) has been introduced to overcome these issues, which helps develop high-performing models using real datasets that are small or slightly different but related to the training data. This paper presents a comprehensive survey of DTL-based ASR frameworks to shed light on the latest developments and helps academics and professionals understand current challenges. Specifically, after presenting the DTL background, a well-designed taxonomy is adopted to inform the state-of-the-art. A critical analysis is then conducted to identify the limitations and advantages of each framework. Moving on, a comparative study is introduced to highlight the current challenges before deriving opportunities for future research.