This review aims to critically examine the existing state-of-the-art forest fire detection systems that are based on deep learning methods. In general, forest fire incidences bring significant negative impact to the economy, environment, and society. One of the crucial mitigation actions that needs to be readied is an effective forest fire detection system that are able to automatically notify the relevant parties on the incidence of forest fire as early as possible. This review paper has examined in details 37 research articles that have implemented deep learning (DL) model for forest fire detection, which were published between January 2018 and 2023. In this paper, in depth analysis has been performed to identify the quantity and type of data that includes images and video datasets, as well as data augmentation methods and the deep model architecture. This paper is structured into five subsections, each of which focuses on a specific application of deep learning (DL) in the context of forest fire detection. These subsections include 1) classification, 2) detection, 3) detection and classification, 4) segmentation, and 5) segmentation and classification. To compare the model's performance, the methods were evaluated using comprehensive metrics like accuracy, mean average precision (mAP), F1-Score, mean pixel accuracy (MPA), etc. From the findings, of the usage of DL models for forest fire surveillance systems have yielded favourable outcomes, whereby the majority of studies managed to achieve accuracy rates that exceeds 90%. To further enhance the efficacy of these models, future research can explore the optimal fine-tuning of the hyper-parameters, integrate various satellite data, implement generative data augmentation techniques, and refine the DL model architecture. In conclusion, this paper highlights the potential of deep learning methods in enhancing forest fire detection that is crucial for forest fire management and mitigation.