This paper presents Slime, a novel non-deep image matching framework which models the scene as rough local overlapping planes. This intermediate representation sits in-between the local affine approximation of the keypoint patches and the global matching based on both geometrical and similarity constraints, providing a progressive pruning of the correspondences, as planes are easier to handle with respect to general scenes. Slime proceeds by selectively detect, expand, merge and refine the matches associated to almost-planar areas of the scene by exploiting homography constraints. As a result, both the coverage and stability of correct matches over the scene are amplified, allowing traditional hybrid matching pipelines to make up lost ground against recent end-to-end deep matching methods. In addition, the paper gives a thorough comparative analysis of recent state-of-the-art in image matching represented by end-to-end deep networks and hybrid pipelines. The evaluation considers both planar and non-planar scenes, taking into account critical and challenging scenarios including abrupt temporal image changes and strong variations in relative image rotations. According to this analysis, although the impressive progress done in this field, there is still a wide room for improvements to be investigated in future research.