We address the problem of camera motion and structure reconstruction from line correspondences across multiple views, from initialization to final bundle adjustment. One of the main difficulties when dealing with line features is their algebraic representation. First, we consider the triangulation problem. Based on Pl?cker coordinates to represent the lines, we propose a maximum likelihood algorithm, relying on linearising the Pl?cker constraint, and on a Pl?cker correction procedure to compute the closest Pl?cker coordinates to a given 6-vector. Second, we consider the bundle adjustment problem. Previous overparameterizations of 3D lines induce gauge freedoms and/or internal consistency constraints. We propose the orthonormal representation, which allows handy non-linear optimization of 3D lines using the minimum 4 parameters, within an unconstrained non-linear optimizer. We compare our algorithms to existing ones on simulated and real data.