The general review on the problem of dark matter and dark energy in observable Universe is given. The problem is treated from the point of view of the research fields on the boundary of which this fundamental task is situated, namely, astrophysics and theoretical physics. We emphasise that interdisciplinary nature of the problem of "dark sector" of Universe can assist in its resolution. The paper does not describe the history of the question, but is centred on revealing the main trends and perspectives.