This is a joint work with Alexander Olshanskii. We study the exponents of the growth and cogrowth of subalgebras and subideals in free Lie algebras. In the case of ideals it is known that the growth of a nonzero ideal of a free Lie algebra is equivalent to the growth of the whole algebra. In the case of finitely generated subalgebras the same can be said about the cogrowth of proper finitely generated subalgebras. The most intriguing case is that of subideals.