Extremely fast rotating molecules whose rotational energy is comparable with the molecular bond strength are known as "superrotors." It has been speculated that superrotors may exhibit a number of unique properties, yet only indirect evidence of these molecular objects has been reported to date. Here we demonstrate the first direct observation of molecular superrotors by detecting coherent unidirectional molecular rotation with extreme frequencies exceeding 10 THz. The technique of an "optical centrifuge" is used to control the degree of rotational excitation in an ultrabroad range of rotational quantum numbers, reaching as high as N = 95 in oxygen and N = 60 in nitrogen. State-resolved detection enables us to determine the shape of the excited rotational wave packet and quantify the effect of centrifugal distortion on the rotational spectrum. Femtosecond time resolution reveals coherent rotational dynamics with increasing coherence times at higher angular momentum. We demonstrate that molecular superrotors can be created and observed in dense samples under normal conditions where the effects of ultrafast rotation on many-body interactions, intermolecular collisions, and chemical reactions can be readily explored.