Fossil and comparative primatological evidence suggest that alterations in the development of prehistoric hominin infants kindled three consecutive evolutionary-developmental (evo-devo) trends that, ultimately, paved the way for the evolution of the human brain and cognition. In the earliest trend, infants' development of posture and locomotion became delayed because of anatomical changes that accompanied the prolonged evolution of bipedalism. Because modern humans have inherited these changes, our babies are much slower than other primates to reach developmental milestones such as standing, crawling, and walking. The delay in ancestral babies' physical development eventually precipitated an evolutionary reversal in which they became increasing unable to cling independently to their mothers. For the first time in prehistory, babies were, thus, periodically deprived of direct physical contact with their mothers. This prompted the emergence of a second evo-devo trend in which infants sought contact comfort from caregivers using evolved signals, including new ways of crying that are conserved in modern babies. Such signaling stimulated intense reciprocal interactions between prehistoric mothers and infants that seeded the eventual emergence of motherese and, subsequently, protolanguage. The third trend was for an extreme acceleration in brain growth that began prior to the last trimester of gestation and continued through infants' first postnatal year (early "brain spurt"). Conservation of this trend in modern babies explains why human brains reach adult sizes that are over three times those of chimpanzees. The fossil record of hominin cranial capacities together with comparative neuroanatomical data suggest that, around 3 million years ago, early brain spurts began to facilitate an evolutionary trajectory for increasingly large adult brains in association with neurological reorganization. The prehistoric increase in brain size eventually caused parturition to become exceedingly difficult, and this difficulty, known as the "obstetrical dilemma", is likely to constrain the future evolution of brain size and, thus, privilege ongoing evolution in neurological reorganization. In modern babies, the brain spurt is accompanied by formation and tuning (pruning) of neurological connections, and development of dynamic higher-order networks that facilitate acquisition of grammatical language and, later in development, other advanced computational abilities such as musical or mathematical perception and performance. The cumulative evidence suggests that the emergence and refinement of grammatical language was a prime mover of hominin brain evolution.