This work is devoted to investigating EEG-based biometric recognition systems. One potential advantage of using EEG signals for person recognition is the difficulty in generating artificial signals with biometric characteristics, thus making the spoofing of EEG-based biometric systems a challenging task. However, more works needs to be done to overcome certain drawbacks that currently prevent the adoption of EEG biometrics in real-life scenarios: 1) usually large number of employed sensors, 2) still relatively low recognition rates (compared with some other biometric modalities), 3) the template ageing effect. The existing shortcomings of EEG biometrics and their possible solutions are addressed from three main perspectives in the thesis: pre-processing, feature extraction and pattern classification. In pre-processing, task (stimuli) sensitivity and noise removal are investigated and discussed in separated chapters. For feature extraction, four novel features are proposed; for pattern classification, a new quality filtering method, and a novel instance-based learning algorithm are described in respective chapters. A self-collected database (Mobile Sensor Database) is employed to investigate some important biometric specified effects (e.g. the template ageing effect; using low-cost sensor for recognition). In the research for pre-processing, a training data accumulation scheme is developed, which improves the recognition performance by combining the data of different mental tasks for training; a new wavelet-based de-noising method is developed, its effectiveness in person identification is found to be considerable. Two novel features based on Empirical Mode Decomposition and Hilbert Transform are developed, which provided the best biometric performance amongst all the newly proposed features and other state-of-the-art features reported in the thesis; the other two newly developed wavelet-based features, while having slightly lower recognition accuracies, were computationally more efficient. The quality filtering algorithm is designed to employ the most informative EEG signal segments: experimental results indicate using a small subset of the available data for feature training could receive reasonable improvement in identification rate. The proposed instance-based template reconstruction learning algorithm has shown significant effectiveness when tested using both the publicly available and self-collected databases.