  The complemented subspace problem asks, in general, which closed subspaces
$M$ of a Banach space $X$ are complemented; i.e. there exists a closed subspace
$N$ of $X$ such that $X=M\oplus N$? This problem is in the heart of the theory
of Banach spaces and plays a key role in the development of the Banach space
theory. Our aim is to investigate some results on complemented subspaces, to
give a history of the subject, and to present some open problems.
