  We use Heegaard Floer homology with twisted coefficients to define numerical
invariants for arbitrary closed 3-manifolds equipped torsion spin$^c$
structures, generalising the correction terms (or $d$--invariants) defined by
Ozsv\'ath and Szab\'o for integer homology 3-spheres and, more generally, for
3-manifolds with standard ${\rm HF}^\infty$. Our twisted correction terms share
many properties with their untwisted analogues. In particular, they provide
restrictions on the topology of 4-manifolds bounding a given 3-manifold.
