Recent developments in single-cell omics technologies have enabled the quantification of molecular profiles in individual cells at an unparalleled resolution. Deep learning, a rapidly evolving sub-field of machine learning, has instilled a significant interest in single-cell omics research due to its remarkable success in analysing heterogeneous high-dimensional single-cell omics data. Nevertheless, the inherent multi-layer nonlinear architecture of deep learning models often makes them `black boxes' as the reasoning behind predictions is often unknown and not transparent to the user. This has stimulated an increasing body of research for addressing the lack of interpretability in deep learning models, especially in single-cell omics data analyses, where the identification and understanding of molecular regulators are crucial for interpreting model predictions and directing downstream experimental validations. In this work, we introduce the basics of single-cell omics technologies and the concept of interpretable deep learning. This is followed by a review of the recent interpretable deep learning models applied to various single-cell omics research. Lastly, we highlight the current limitations and discuss potential future directions. We anticipate this review to bring together the single-cell and machine learning research communities to foster future development and application of interpretable deep learning in single-cell omics research.