The Brain-Computer Interface (BCI) systems involve direct human brain communication with other devices by deciphering the neural activity pattern. Electroencephalography (EEG) is very popular among other methods used in neuroimaging because of its non-invasiveness, high time resolution, portability, as well as low cost. EEG signals on the other hand are very complex, non-linear and vulnerable to noise and artifacts and therefore, analysis and classification is difficult. The paper is a detailed research of the EEG signal analysis in the context of BCI application as it entails signal acquisition, preprocessing, feature extraction and classification. The classical models of machine learning, which include Support Vector Machines (SVM), Linear Discriminant Analysis (LDA), Artificial Neural Networks (ANN) are addressed as well as modern deep learning models including Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), hybrid deep models, and transformer-based designs. New trends in wearable EEG and real-time BCI are also discussed. The research paper presents the significance of effective pre-processing, spatial filtering and smart classification methodologies to improve the accuracy and reliability of the systems. The results indicate that deep learning and attention-based methods have a significant effect on enhanced performance in complicated BCI tasks on which they are likely to be a solution to the next-generation EEG-based BCI systems.