Among the many radiation hazards of manned spaceflight is the potential exposure of crew members to neutrons. These neutrons are produced from several sources: from the terrestrial albedo and as secondary particles produced by the interaction of cosmic rays, solar protons and trapped protons with the material of the spacecraft. Recently, neutrons have also been observed originating in solar flares, at the solar surface. Theoretical estimates and experimental measurements of the neutron fluxes inside manned spacecraft in near-Earth orbit are reviewed and discussed. The anticipated neutron fluxes and their resulting dose-equivalents, as a function of shielding depth for exploration class missions, are presented and discussed.