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Regression problems have been more and more embraced by deep learning (DL) techniques. The increasing number of papers recently published in this domain, including surveys and reviews, shows that deep regression has captured the attention of the community due to efficiency and good accuracy in systems with high-dimensional data. However, many DL methodologies have complex structures that are not readily transparent to human users. Accessing the interpretability of these models is an essential factor for addressing problems in sensitive areas such as cyber-security systems, medical, financial surveillance, and industrial processes. Fuzzy logic systems (FLS) are inherently interpretable models, well known in the literature, capable of using nonlinear representations for complex systems through linguistic terms with membership degrees mimicking human thought. Within an atmosphere of explainable artificial intelligence, it is necessary to consider a trade-off between accuracy and interpretability for developing intelligent models. This paper aims to investigate the state-of-the-art on existing methodologies that combine DL and FLS, namely deep fuzzy systems, to address regression problems, configuring a topic that is currently not sufficiently explored in the literature and thus deserves a comprehensive survey.