Derivations into ideals of a von Neumann algebra

One of the classic problems in operator algebra theory is the following: Let $\mathcal{A}$ be an algebra and $J$ be $\mathcal{A}$-bimodule. For which classes of $\mathcal{A}$-bimodules $J$ every derivation $\delta: \mathcal{A} \to J$ is inner, i.e., can we find an $x\in J$ such that $\delta(a) = [x,a]$? The report gives an overview of the results that give a solution of this problem in the case when $\mathcal{A}$ is a von Neumann algebra and $J$ is an ideal in $\mathcal{A}$.