This is an announcement for the paper "On almost-invariant subspaces and approximate commutation" by Laurent W. Marcoux, Alexey I. Popov, and Heydar Radjavi. Abstract: A closed subspace of a Banach space $\cX$ is almost-invariant for a collection $\cS$ of bounded linear operators on $\cX$ if for each $T \in \cS$ there exists a finite-dimensional subspace $\cF_T$ of $\cX$ such that $T \cY \subseteq \cY + \cF_T$. In this paper, we study the existence of almost-invariant subspaces of infinite dimension and codimension for various classes of Banach and Hilbert space operators. We also examine the structure of operators which admit a maximal commuting family of almost-invariant subspaces. In particular, we prove that if $T$ is an operator on a separable Hilbert space and if $TP-PT$ has finite rank for all projections $P$ in a given maximal abelian self-adjoint algebra $\fM$ then $T=M+F$ where $M\in\fM$ and $F$ is of finite rank. Archive classification: math.FA math.OA Mathematics Subject Classification: 47A15, 47A46, 47B07, 47L10 Submitted from: a4popov@uwaterloo.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1204.4621 or http://arXiv.org/abs/1204.4621