This chapter discusses how the electroencephalography (EEG) and magnetoencephalography (MEG) methods have been used to study the multilingual brain. It introduces the methods, the physiological basis of the data obtained from them, and the advantages and disadvantages of the methods compared to each other and to other neuroimaging techniques. The chapter briefly presents how these techniques have been used to address questions about the multilingual brain. The most common way of analysing continuously recorded language-related EEG and MEG data is to extract event-related potentials (ERPs) or event-related fields (ERFs), respectively. In a neurocognitive framework, the mastery of a second language is thought to involve the ability not only to represent linguistic knowledge, but also to process linguistic input in a native-like manner. The chapter briefly presents a sample of studies that have measured the brain signatures for language switching, first in production then during written sentence comprehension, in bilinguals and professional simultaneous interpreters.