A surprisingly large "organic magnetoresistance" (OMAR) has been found in both polymers and small molecule organic semiconductors at relatively small applied magnetic fields and at room temperature. We review recent highlights in OMAR research and discuss some of the models that have been proposed to explain the effect. In all models spin dephasing due to hyperfine fields plays an essential role. In particular we focus on the characteristic magnetic field dependence, which is generally fitted with either a Lorentzian or a so-called non-Lorentzian function. The shape is determined by both the hyperfine fields and an additional broadening due to microscopic mechanisms, as described in the models. Within the present work, a new empirical function is introduced that captures the two effects separately and converges to the earlier introduced lineshapes in specific limits. Recently it has been demonstrated that an additional feature can be observed at ultra-small magnetic fields. This effect can be easily incorporated in our empirical approach by explicitly treating the limit in which hopping of carriers is no longer slow compared to spin precession in the hyperfine fields. Our approach is used to analyze several theoretical and experimental results. It is shown that experimentally observed trends can be well-understood and important parameters can be obtained from experimental data without prior knowledge about which model applies.