Electroencephalography (EEG) is a non-invasive neurophysiological monitoring technique. It records the electrical activity of the cerebral cortex using electrodes placed on the scalp surface. Owing to its high safety, portability, and millisecond-level temporal resolution, EEG has been widely utilized in a variety of fields, including clinical diagnosis, brain-computer interfaces (BCIs), and cognitive neuroscience research. However, due to its microvolt-level amplitude, EEG is highly susceptible to various artifacts, including electrooculographic (EOG), electrocardiographic (ECG), electromyographic (EMG), and power line interference (PLI). These artifacts can obscure genuine neural activity and introduce spurious electrophysiological features. Consequently, they may compromise EEG signal quality, thereby reducing the reliability of downstream analyses. To address this issue, numerous EEG artifact removal methods have been developed, including both traditional denoising techniques and deep learning-based approaches. Traditional EEG denoising methods have long served as the primary solutions for artifact removal. Representative approaches include filtering, regression, and blind source separation. Although these methods have demonstrated effectiveness in specific scenarios, they suffer from several inherent limitations. Filtering assumes that artifacts and EEG signals can be separated in the frequency domain, but many artifacts, such as EOG and EMG, overlap with EEG spectra, which may lead to the loss of valuable neural information. Regression methods require high-quality artifact references to estimate and subtract contaminations, limiting their effectiveness in reference-free scenarios. Blind source separation can remove artifacts without external references, but it typically requires the number of EEG channels to exceed the number of sources, restricting its application in single- or low-channel EEG recordings. Deep learning-based EEG denoising methods address these limitations effectively. First, they learn the nonlinear mapping between contaminated and clean EEG directly from data in an end-to-end manner. This approach does not rely on assumptions about spectral separability, thereby preserving neural activity more completely. Second, the reference information is incorporated during the training phase, allowing the trained model to perform artifact removal independently without external references. Third, deep learning models can be flexibly designed to accommodate various recording setups, achieving robust denoising for both high-density and single-channel EEG. Collectively, these advantages enable deep learning-based methods to overcome the main challenges of traditional approaches, providing more accurate and reliable EEG signal recovery. The superior denoising performance of deep learning-based EEG denoising methods has attracted increasing attention in EEG artifact removal research. As a result, many deep learning-based denoising methods have been developed and successfully applied in neural engineering areas. However, a systematic review of the techniques and applications in this field is still lacking. To address this gap, this paper reviews recent advances in deep learning-based EEG denoising from four perspectives: technical principle, benchmark dataset, denoising model, and evaluation method. Representative applications in neural signal analysis and BCI decoding are also summarized. Furthermore, the advantage, existing challenge, and future research direction of deep learning-based EEG denoising are discussed. This review aims to provide valuable theoretical insights and technical guidance for researchers. It is also expected to promote further advances and broader applications of deep learning-based EEG denoising techniques.