Deep learning has been extensively employed for predicting the remaining useful life (RUL) of equipment owing to the powerful feature extraction ability of deep learning. However, the deep learning prediction results are often affected by random noise, modeling parameters, and other factors, considerably reducing the credibility of point predictions. This reduction may lead to inappropriate decisions and sometimes even cause equipment operation collapse. Therefore, the key to ensuring the smooth progress of the entire industrial production process is accurately quantifying the uncertainties transmitted in the output of the RUL prediction model and forming an effective and reasonable maintenance decision plan. The prediction interval is a statistical measure used to quantify uncertainty in predictions. The prediction interval comprises the upper and lower prediction bounds between which an unknown value is expected with a specific probability. The option of prediction intervals enables decision-makers and operational planners to effectively quantify the uncertainty level associated with point predictions and consider multiple solutions for optimal and worst-case conditions. A wide prediction interval indicates a high degree of uncertainty in the underlying system operation. This information signals decision-makers to avoid choosing risky actions under uncertain conditions. By contrast, a narrow prediction interval implies that decisions can be made with more confidence and unexpected situations will be less in the future. The aim of this paper is to analyze and elaborate the basic ideas and development trends of current deep learning-based RUL interval prediction models to provide a good reference for exploring implementable deep learning-based RUL interval prediction model that is highly reliable, cost-efficient, and easy. Thus, while facing the practical demand of uncertainty quantification in the modeling of equipment RUL based on deep learning, this paper first analyzes the sources of uncertainty in RUL prediction, such as data quality, model error, and changes in model parameters and the external environment. Subsequently, five popular deep learning-based RUL interval prediction models are presented: bootstrap deep learning, local uncertainty, stochastic process deep learning, Bayesian deep learning, and deep learning quantile regression. Through the model establishment process and current development status analysis, the advantages and disadvantages of the five RUL interval prediction models are summarized. Finally, the challenges encountered during the current research on the RUL interval prediction of equipment based on deep learning and potential future research directions are explored.