The idea of studying multi-view geometry and structure-from-motion problems {\em relative} to the scene and camera configurations, without appeal to external coordinate systems, dates back to the early days of modern geometric computer vision. Yet, it has a bad rap, the scene reconstructions obtained often being deemed as inaccurate despite careful implementations. The aim of this article is to correct this perception with a series of new results. In particular, we show that using a small subset of scene and image points to parameterize their relative configurations offers a natural coordinate-free formulation of Carlsson-Weinshall duality for arbitrary numbers of images. For three views, this approach also yields novel purely- and quasi-linear formulations of structure from motion using {\em reduced trilinearities}, without the complex polynomial constraints associated with trifocal tensors, revealing in passing the strong link between ``3D''($\mathbb P^3\rightarrow\mathbb P^2$) and ``2D'' ($\mathbb P^2\rightarrow\mathbb P^1$) models of trinocular vision. Finally, we demonstrate through preliminary experiments that the proposed relative reconstruction methods gives good results on real data.