In this work, we present and analyse the Hough transform (HT) to recognise and approximate space curves in 3D digital models, a problem that is not currently addressed by the standard HT. We introduce a method that is able to handle both with families of curves expressed in parametric and implicit form, assuming some hypotheses on the type of equations. We also extend the existing dictionary of space curves by introducing a new family type that takes advantage of the rich template of plane curves.