Wall's D(2) problem

Let $X$ be a finite $3$-dimensional CW complex whose cohomological dimension is at most $2$. Wall's D(2) problem. $X$ is homotopy equivalent to a $2$-dimensional CW complex. The problem is stated as very difficult in general and is known for only a limited amount of groups. A positive answer would imply a finite version of the Eilenberg–Ganea conjecture.