In the light of the very massive neutron stars recently detected and the new possible constraints for the radii of these compact objects, we revisit some equations of state obtained for hadronic and hybrid stars under the influence of strong magnetic fields. We present our results for hadronic matter, taking into account the effects of the inclusion of anomalous magnetic moment. Additionally, the case of hybrid stars under the influence of strong magnetic fields is considered. We study the structure of hybrid stars based on the Maxwell condition (without a mixed phase), where the hadron phase is described by the nonlinear Walecka model (NLW) and the quark phase by the Nambu-Jona-Lasinio model (NJL). The mass-radius relations for all cases are calculated and discussed. We show that both hadronic and hybrid stars can bear very high masses and radii, compatible with the recently observed high-mass neutron stars. © 2014 American Physical Society.