This chapter explains the genesis of inequalities and hierarchies in modern science. It studies the forms and mechanisms of scientific communication on the basis of which the social structures of science are built: publications, authorship, co- and multiple authorship, citations as units of information and as social rewards, peer review as evaluation of publications (and of projects and careers). This is a network of institutions that seems to guarantee universal access to participation in science to all those who fulfill basic conditions. But the chapter demonstrates how in all these institutional dimensions differences arise between successful and not equally successful participations. Success generates influence and social attractiveness (e.g. as a co-author). Influential and attractive participants are recruited into positions where they assess the achievements of others and thereby limit and control inclusion in publications, funding and careers. Equality at the start is transformed into hierarchies of control. Finally, the chapter asks for potential alternative control structures that transform a conservative hierarchy into decentralized ‘market’ controls that involve everyone in a more dynamic production and evaluation of scientific achievements.