One of the objectives of the CoRoT mission is the search for transiting extrasolar planets using high-precision photometry, and the accurate characterization of their fundamental parameters. The CoRoT satellite consecutively observes crowded stellar fields since February 2007, in high-cadence precise photometry; periodic eclipses are detected and analyzed in the stellar light curves. Then complementary observations using ground-based facilities allows establishing the nature of the transiting body and its mass. CoRoT has acquired more than 163,000 light curves and detected about 500 planet candidates. A fraction of them (5%) are confirmed planets whose masses are independently measured. Main highlights of the CoRoT discoveries are: (i) the variety of internal structures in close-in giant planets, (ii) the characterization of the first known transiting rocky planet, CoRoT-7b, and (iii) multiple constraints on the formation, evolution, role of tides in planetary systems.