Many nearby main-sequence stars have been searched for debris using the far-infrared Herschel satellite, within the DEBRIS, DUNES and Guaranteed-Time Key Projects.We discuss here 11 stars of spectral types A to M where the stellar inclination is known and can be compared to that of the spatially-resolved dust belts. The discsare found to be well aligned with the stellar equators, as in the case of the Sun’s Kuiper belt, and unlike many close-in planets seen in transit surveys. The ensemble of stars here can be fitted with a star-disc tilt of ≲10º. These results suggest that proposed mechanisms for tilting the star or disc in fact operate rarely. A few systems also host imaged planets, whose orbits at tens of AU are aligned with the debris discs, contrary to what might be expected in models where external perturbers induce tilts.