Recent methods that allow a noninvasive modulation of brain activity are able to modulate human cognitive behavior. Among these methods are transcranial electric stimulation and transcranial magnetic stimulation that both come in multiple variants. A property of both types of brain stimulation is that they modulate brain activity and in turn modulate cognitive behavior. Here, we describe the methods with their assumed neural mechanisms for readers from the economic and social sciences and little prior knowledge of these techniques. Our emphasis is on available protocols and experimental parameters to choose from when designing a study. We also review a selection of recent studies that have successfully applied them in the respective field. We provide short pointers to limitations that need to be considered and refer to the relevant papers where appropriate.