  Using orbifold metrics of the appropriately signed Ricci curvature on
orbifolds with negative or numerically trivial canonical bundle and the
two-dimensional Log Minimal Model Program, we prove that the fundamental group
of special compact K\"ahler threefolds is almost abelian. This property was
conjectured in all dimensions in [Cam04b], and also for orbifolds in [Cam07],
where the notion of specialness was introduced. We briefly recall below the
definition, basic properties, and the role of special manifolds in
classification theory.
