Electroencephalography (EEG) and functional Magnetic Resonance Imaging (MRI) have long been used as tools to examine brain activity. Since both methods are very sensitive to changes of synaptic activity, simultaneous recording of EEG and fMRI can provide both high temporal and spatial resolution. Therefore, the two modalities are now integrated into a hybrid tool, EEG-fMRI, which encapsulates the useful properties of the two. Among other benefits, EEG-fMRI can contribute to a better understanding of brain connectivity and networks. This review lays its focus on the methodologies applied in performing EEG-fMRI studies, namely techniques used for the recording of EEG inside the scanner, artifact removal, and statistical analysis of the fMRI signal. We will investigate simultaneous resting-state and task-based EEG-fMRI studies and discuss their clinical and technological perspectives. Moreover, it is established that the brain regions affected by a task-based neural activity might not be limited to the regions in which they have been initiated. Advanced methods can help reveal the regions responsible for or affected by a developed neural network. Therefore, we have also looked into studies related to characterization of structure and dynamics of brain networks. The reviewed literature suggests that EEG-fMRI can provide valuable complementary information about brain neural networks and functions.