The theory of the s process of nucleosynthesis has received considerable development during recent years, mainly as the result of more detailed physical and mathematical treatments and also as a result of the accumulation of new observational data on stellar evolution and the abundance of the elements in the solar system, and accumulation of experimental data on neutron-capture cross sections. The exact solution of the s process equations obtained recently by Newman (1978) is discussed. It confirms the correctness of the initial s process theory (Clayton, Fowler, Hull, and Zimmerman, 1961). At the same time for small neutron exposures the exact and initial solutions differ. The influence of branching of the s-process due to competition between β decay and neutron capture is analyzed; it is noted that at a temperature ~3·108 K and a density of free neutrons 1.6·107 cm−3 the s process theory is in good agreement with observational data on the yields of the various nuclides. Models are discussed for the pulsed neutron s process, which leads to formation of heavy elements in the interior of a star as the result of periodic flares of the helium shell and subsequent remixing of the material.