  A variant of the quantum marginal problem was known from early sixties as
N-representability problem. In 1995 it was designated by National Research
Council of USA as one of ten most prominent research challenges in quantum
chemistry. In spite of this recognition the progress was very slow, until a
couple of years ago the problem came into focus again, now in framework of
quantum information theory. In the paper I give an account of the recent
development.
