Man's natural inclination to classify and hierarchize the living world has prompted neurophysiologists to explore possible differences in brain organisation between mammals, with the aim of understanding the diversity of their behavioural repertoires. But what really distinguishes the human brain from that of a platypus, an opossum or a rodent? In this review, we compare the structural and electrical properties of neocortical neurons in the main mammalian radiations and examine their impact on the functioning of the networks they form. We discuss variations in overall brain size, number of neurons, length of their dendritic trees and density of spines, acknowledging their increase in humans as in most large-brained species. Our comparative analysis also highlights a remarkable consistency, particularly pronounced in marsupial and placental mammals, in the cell typology, intrinsic and synaptic electrical properties of pyramidal neuron subtypes, and in their organisation into functional circuits. These shared cellular and network characteristics contribute to the emergence of strikingly similar large-scale physiological and pathological brain dynamics across a wide range of species. These findings support the existence of a core set of neural principles and processes conserved throughout mammalian evolution, from which a number of species-specific adaptations appear, likely allowing distinct functional needs to be met in a variety of environmental contexts.