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Deep learning, a crucial technique for achieving artificial intelligence (AI), has been successfully applied in many fields. The gradual application of the latest architectures of deep learning in the field of time series forecasting (TSF), such as Transformers, has shown excellent performance and results compared to traditional statistical methods. These applications are widely present in academia and in our daily lives, covering many areas including forecasting electricity consumption in power systems, meteorological rainfall, traffic flow, quantitative trading, risk control in finance, sales operations and price predictions for commercial companies, and pandemic prediction in the medical field. Deep learning-based TSF tasks stand out as one of the most valuable AI scenarios for research, playing an important role in explaining complex real-world phenomena. However, deep learning models still face challenges: they need to deal with the challenge of large-scale data in the information age, achieve longer forecasting ranges, reduce excessively high computational complexity, etc. Therefore, novel methods and more effective solutions are essential. In this paper, we review the latest developments in deep learning for TSF. We begin by introducing the recent development trends in the field of TSF and then propose a new taxonomy from the perspective of deep neural network models, comprehensively covering articles published over the past five years. We also organize commonly used experimental evaluation metrics and datasets. Finally, we point out current issues with the existing solutions and suggest promising future directions in the field of deep learning combined with TSF. This paper is the most comprehensive review related to TSF in recent years and will provide a detailed index for researchers in this field and those who are just starting out. [ABSTRACT FROM AUTHOR]