We study the problem of aligning two 3D line reconstructions expressed in Plücker line coordinates. We introduce the 6×6 3D line motion matrix that acts on Plucker coordinates in projective, affine or Euclidean space. We characterize its algebraic properties and its relation to the usual 4×4 point motion matrix, and propose various methods for estimating 3D motion from line correspondences, based on image-related and 3D cost functions. We assess the quality of the different estimation methods using simulated data and real images.