A multi-paradigm approach integrating three novel computational paradigms: wavelet transforms, chaos theory, and artificial neural networks is developed for EEG-based epilepsy diagnosis and seizure detection. This research challenges the assumption that the EEG represents the dynamics of the entire brain as a unified system. It is postulated that the sub-bands yield more accurate information about constituent neuronal activities underlying the EEG. Consequently, certain changes in EEGs not evident in the original full-spectrum EEG may be amplified when each sub-band is analyzed separately. A novel wavelet-chaos methodology is presented for analysis of EEGs and delta, theta, alpha, beta, and gamma sub-bands of EEGs for detection of seizure and epilepsy. The methodology is applied to three different groups of EEGs: healthy subjects, epileptic subjects during a seizure-free interval (interictal), and epileptic subjects during a seizure (ictal). Two potential markers of abnormality quantifying the non-linear chaotic EEG dynamics are discovered: the correlation dimension and largest Lyapunov exponent. A novel wavelet-chaos-neural network methodology is developed for EEG classification. Along with the aforementioned two parameters, the standard deviation (quantifying the signal variance) is employed for EEG representation. It was discovered that a particular mixed-band feature space consisting of nine parameters and LMBPNN result in the highest classification accuracy (96.7%). To increase the robustness of classification, a novel principal component analysis-enhanced cosine radial basis function neural network classifier is developed. The rearrangement of the input space along the principal components of the data improves the classification accuracy of the cosine radial basis function neural network employed in the second stage significantly. The new classifier is as accurate as LMBPNN and is twice as robust. Next, biologically realistic artificial neural networks are developed to reach the next milestone in artificial intelligence. First, an efficient spiking neural network (SNN) model is presented using three training algorithms: SpikeProp, QuickProp, and RProp. Three measures of performance are investigated: number of convergence epochs, computational efficiency, and classification accuracy. Next, a new Multi-Spiking Neural Network (MuSpiNN) and supervised learning algorithm (Multi-SpikeProp) are developed. Finally, the models are applied to the epilepsy and seizure detection problems to achieve high classification accuracies.