This paper presents a comprehensive review of various statistical, machine learning, and deep learning methods for quantile regression in time series, focusing on their application in predicting dengue outbreaks. Given the increasing global incidence of dengue, the ability to forecast higher quantiles of cases is crucial for effective public health responses. The study emphasizes the limitations of traditional regression models, which typically predict average outcomes, and instead highlights the importance of probabilistic forecasting methods that account for uncertainty, offering more detailed predictions for extreme events. Methods such as quantile autoregression (QAR), quantile neural networks, penalized quantile regression and hybrid models are evaluated through simulations and are applied to a real-world dataset from a dengue-prone region. The study also discusses the potential of recent advances, including deep reinforcement learning, in quantile regression forecasts under various scenarios. The performances of these models are assessed using metrics like root mean squared error and continuous ranked probability score, with QAR consistently outperforming other models in real-life scenario and LASSO-based quantile regression providing excellent results in various simulation settings.