Inclusive one-hadron production cross sections provide valuable information about various aspects of QCD including perturbative and nonperturbative physics. New measurements at the LHC provide new opportunities to test our knowledge to new frontier. In order to obtain useful information from LHC measurements, it is important to have an understanding of hadron production mechanisms in hard collisions. Production cross sections of heavy flavored hadrons and heavy quarkonium contain the heavy quark mass as a hard scale, which lets us apply perturbation theory at the scale of the mass of the produced hadron. While this becomes an advantage when we want to take more theoretical control over hadron production mechanisms, approaches based on solid theoretical ground can sometimes become unsatisfactory. In this paper, we review the current status of heavy flavor and quarkonium production mechanisms that are popularly used to describe LHC data.