In this talk I will describe categories of representations of the infinite-dimensional algebras sl(∞), o(∞), sp(∞) analogous to the category of finite dimensional representations of a simple Lie algebra. It is important that these categories are not semisimple but Koszul. Another interesting fact is that the respective categories for o(∞) and sp(∞) are equivalent as tensor categories. Joint work with V. Serganova and E. Dan-Cohen.