Emotions are a series of subconscious, fleeting, and sometimes elusive manifestations of the human innate system. They play crucial roles in everyday life—influencing the way we evaluate ourselves, our surroundings, and how we interact with our world. To date, there has been an abundance of research on the domains of neuroscience and affective computing, with experimental evidence and neural network models, respectively, to elucidate the neural circuitry involved in and neural correlates for emotion recognition. Recent advances in affective computing neural network models often relate closely to evidence and perspectives gathered from neuroscience to explain the models. Specifically, there has been growing interest in the area of EEG-based emotion recognition to adopt models based on the neural underpinnings of the processing, generation, and subsequent collection of EEG data. In this respect, our review focuses on providing neuroscientific evidence and perspectives to discuss how emotions potentially come forth as the product of neural activities occurring at the level of subcortical structures within the brain’s emotional circuitry and the association with current affective computing models in recognizing emotions. Furthermore, we discuss whether such biologically inspired modeling is the solution to advance the field in EEG-based emotion recognition and beyond.