Aggression is a social behavior essential for securing resources and defending oneself and family. Thanks to its indispensable function in competition and thus survival, aggression exists widely across animal species, including humans. Classical works from Tinbergen and Lorenz concluded that instinctive behaviors including aggression are mediated by hardwired brain circuitries that specialize in processing certain sensory inputs to trigger stereotyped motor outputs. They further suggest that instinctive behaviors are influenced by an animal's internal state and past experiences. Following this conceptual framework, here we review our current understanding regarding the neural substrates underlying aggression generation, highlighting an evolutionarily conserved 'core aggression circuit' composed of four subcortical regions. We further discuss the neural mechanisms that support changes in aggression based on the animal's internal state. We aim to provide an overview of features of aggression and the relevant neural substrates across species, highlighting findings in rodents, primates and songbirds.