This paper presents the effectiveness of bioelectrical signals such as the electrocardiogram (ECG) and the electroencephalogram (EEG) for biometric applications. Studies show that the impulses of cardiac rhythm and electrical activity of the brain recorded in ECG and EEG, respectively; have unique features among individuals, therefore they can be suggested to be used as biometrics for identity verification. The favourable characteristics to use the ECG or EEG signals as biometric include universality, measurability, uniqueness and robustness. In addition, they have the inherent feature of vitality that signifies the life signs offering a strong protection against spoof attacks. Unlike conventional biometrics, the ECG or EEG is highly confidential and secure to an individual which is difficult to be forged. We present a review of methods used for the ECG and EEG as biometrics for individual authentication and compare their performance on the datasets and test conditions they have used. We illustrate the challenges involved in using the ECG or EEG as biometric primarily due to the presence of drastic acquisition variations and the lack of standardization of signal features. In order to determine the large-scale performance, individuality of the ECG or EEG is another challenge that remains to be addressed.