A novel algorithm for wide-baseline matching called MODS - Matching On Demand with view Synthesis - is presented. The MODS algorithm is experimen- tally shown to solve a broader range of wide-baseline problems than the state of the art while being nearly as fast as standard matchers on simple problems. The apparent robustness vs. speed trade-off is finessed by the use of progres- sively more time-consuming feature detectors and by on-demand generation of synthesized images that is performed until a reliable estimate of geometry is obtained. We introduce an improved method for tentative correspondence selection, applicable both with and without view synthesis. A modification of the standard first to second nearest distance rule increases the number of correct matches by 5-20% at no additional computational cost. Performance of the MODS algorithm is evaluated on several standard pub- licly available datasets, and on a new set of geometrically challenging wide base- line problems that is made public together with the ground truth. Experiments show that the MODS outperforms the state-of-the-art in robustness and speed. Moreover, MODS performs well on other classes of difficult two-view problems like matching of images from different modalities, with wide temporal baseline or with significant lighting changes.