While the existing deep neural networks have earned great successes in various application scenarios，they are still facing black-box challenges that they are not very suitable for some application fields such as healthcare， finance and transportation. Therefore， explainable artificial intelligence （XAI） has been becoming a hot research topic in recent years. Among the existing XAI means， since fuzzy AI systems have the impressive ability to achieve an excellent trade-off between performance and interpretability，interpretable deep Takagi-Sugeno-Kang （TSK） fuzzy systems have been drawing more and more attentions. We first state the concept of the classical TSK fuzzy systems，then give a comprehensive overview of interpretable deep TSK fuzzy systems which are based on stacked generalization principle， including their structures，representative models and application scenarios， and finally discuss their future development direction according to their existing problems.