Born in Moscow, he graduated from the Biology and Chemistry Faculty of MGZPI (now the Sholokhov Moscow State University for Humanities), worked at the Brain Institute of the USSR Academy of Medical Sciences, since 1984 at the Institute of Human Morphology RAMS. The author of the idea of cerebral sorting.
For more than 30 years Sergey Savelyev conducts research in the field of morphology and evolution of the brain. The author of more than 10 books, 100 scientific articles and the world's first Stereoscopic Atlas of the Human Brain, which was awarded the prize of V.N. Shevkunenko RAMS for the best scientific work on "Topographical anatomy and operative surgery" for 2001.
For many years engaged in the study of fetal pathologies of the nervous system, he develops methods of their diagnosis. He identified the basic principles of emergence of neurulation abnormalities of the nervous system in humans and animals. For the first time he examined and photographed the 11-day human embryo. With accuracy to the days he determined the crisis phases in the formation of the nervous system of the embryo, leading to the different pathologies of the human brain. He studied the molecular mechanisms of morphogenetic information coding in the embryonic nervous system. He created and experimentally confirmed the positional control theory of the early embryonic development of the vertebrates brain, proving that in the early stages of development, there is no rigid genetic determination (cell fate is determined not by the genome, but by cell-cell biomechanical interactions). In 2002 he published a monograph, illustrating it with original snapshots of entire human embryos in the first days after implantation and neurulation period.
Considerable attention he paid to the origin of the nervous system and its evolution, introduced evolutionary theory of transitional environments as a basis for the development of neurobiological models of the origin of chordates, protoaquatic vertebrates, amphibians, reptiles, birds and mammals, gave examples of the use of neurobiological laws for the reconstruction of the ways of the evolution of vertebrates and invertebrates. He developed the basic principles of adaptive evolution of the nervous system and behavior.
He investigated the reasons and evolutionary regularities of development of the forebrain and neocortex of mammals. He described morphological and functional features of the early evolution of primate brain. Based on the analysis of the hominid brain structure he developed neurobiological hypotheses of occurrence of bipedality, association and speech centers development, established neurobiological regularities of emergence of the brain of modern human.
For many years he is engaged in research in the field of paleoneurology with the Paleontological Institute of Russian Academy of Sciences. Together with senior scientists of the Institute A.V. Lavrov (laboratory of mammals) and V.R. Alifanov (laboratory of paleoherpetology) he established the principles of brain organization of dinosaurs, creodonts and gienodonts. He developed a hypothesis of the origin of protofeathers from the skin appendages (setigerous scales) of Late Jurassic dinosaurs.
In 2009, he developed a method to identify the hidden signs of schizophrenia based on the presence or absence of stones and empty cavities in the epiphysis.
In 2013 he headed the working group to study the brain of a mammoth, which included employees of the Research Institute of Human Morphology RAMS, Yakutsk Academy of Sciences and the Paleontological Institute RAS. Under his leadership in 2014 was created the world's first three-dimensional model of the brain of a mammoth.
In 2014, he led the experiment "Gecko-F4", the purpose of which was to study the effect of microgravity on the sexual behavior, the body of adult animals and the embryonic development of geckos Phelsuma ornata in a two-month orbital experiment on the Russian research satellite "Foton-M No.4".
Sergey Savelyev is the author of the idea of cerebral sorting - a method of analysis of individual human capacities on the brain structures through the development and application of a high-resolution tomograph. The idea is based on his many years experience of research work in the field of cerebral cortex cytoarchitectonics, as well as individual variability of the architectonics and subcortical brain structures and also morphological foundations of human endowments, held at the Brain Institute of the Academy of Medical Sciences of the USSR.