Deep learning has been widely applied in predicting the remaining useful life (RUL) of equipment due to its powerful feature extraction ability. However, the prediction results of deep learning are often affected by random noise, modeling parameters and other factors, greatly reducing the credibility of point predictions, which may lead to inappropriate decisions and sometimes even cause equipment operation collapse. Therefore, accurate RUL interval prediction is crucial for understanding the randomness of equipment degradation processes and making reliable risk analysis and maintenance decisions. Facing the practical demand of uncertainty quantification in equipment RUL modeling under the background of deep learning, this paper focuses on the basic ideas and development trends of RUL interval prediction models such as bootstrap deep learning, local uncertainty, stochastic process deep learning, Bayesian deep learning, and deep learning quantile regression. Also, the corresponding advantages and disadvantages are summarized. Finally, the challenging issues faced in the current research on equipment RUL interval prediction based on deep learning and potential future research directions are explored.