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This review provides a high-level synthesis of significant recent advances in artificial neural network research, as well as multi-disciplinary concepts connected to the far-reaching goal of obtaining intelligent systems. We assume that a global outlook of these interconnected fields can benefit researchers by providing alternative viewpoints. Therefore, we present different network and neuron models, we discuss model parameters and the means to obtain them, and we draw a quick outline of information encoding, before proceeding to an overview of the relevant learning mechanisms, ranging from established approaches to novel ideas. We specifically focus on comparing the classical artificial model with the biologically-feasible spiking neuron, and we take this comparison further into a discussion on the biological plausibility of various learning approaches.