It has been experimentally discovered that a low magnetic field (less than 500 mT) can substantially change the electroluminescence, photoluminescence, photocurrent, and electrical-injection current in nonmagnetic organic semiconducting materials, leading to magnetic-field effects (MFEs). Recently, there has been significant driving force in understanding the fundamental mechanisms of magnetic responses from nonmagnetic organic materials because of two potential impacts. First, MFEs can be powerful experimental tools in revealing and elucidating useful and non-useful excited processes occurring in organic electronic, optical, and optoelectronic devices. Second, MFEs can lead to the development of new multifunctional organic devices with integrated electronic, optical, and magnetic properties for energy conversion, optical communication, and sensing technologies. This progress report discusses magnetically sensitive excited states and charge-transport processes involved in MFEs. The discussions focus on both fundamental theories and tuning mechanisms of MFEs in nonmagnetic organic semiconducting materials.