Electroencephalography (EEG) is increasingly important in Brain-Computer Interface (BCI) systems due to its portability and simplicity. In this paper, we provide a comprehensive review of research on EEG signal processing techniques since 2021, with a focus on preprocessing, feature extraction, and classification methods. We analyzed 61 research articles retrieved from academic search engines, including CNKI, PubMed, Nature, IEEE Xplore, and Science Direct. For preprocessing, we focus on innovatively proposed preprocessing methods, channel selection, and data augmentation. Data augmentation is classified into conventional methods (sliding windows, segmentation and recombination, and noise injection) and deep learning methods [Generative Adversarial Networks (GAN) and Variation AutoEncoder (VAE)]. We also pay attention to the application of deep learning, and multi-method fusion approaches, including both conventional algorithm fusion and fusion between conventional algorithms and deep learning. Our analysis identifies 35 (57.4%), 18 (29.5%), and 37 (60.7%) studies in the directions of preprocessing, feature extraction, and classification, respectively. We find that preprocessing methods have become widely used in EEG classification (96.7% of reviewed papers) and comparative experiments have been conducted in some studies to validate preprocessing. We also discussed the adoption of channel selection and data augmentation and concluded several mentionable matters about data augmentation. Furthermore, deep learning methods have shown great promise in EEG classification, with Convolutional Neural Networks (CNNs) being the main structure of deep neural networks (92.3% of deep learning papers). We summarize and analyze several innovative neural networks, including CNNs and multi-structure fusion. However, we also identified several problems and limitations of current deep learning techniques in EEG classification, including inappropriate input, low cross-subject accuracy, unbalanced between parameters and time costs, and a lack of interpretability. Finally, we highlight the emerging trend of multi-method fusion approaches (49.2% of reviewed papers) and analyze the data and some examples. We also provide insights into some challenges of multi-method fusion. Our review lays a foundation for future studies to improve EEG classification performance.