In this chapter we will explore the motivation for simultaneous measurements of electroencephalography (EEG) together with functional magnetic resonance imaging (fMRI), termed EEG-fMRI. When measured together, these modalities provide a unique opportunity to measure human brain activity with a level of precision in space and time that is not possible with each modality alone. However, recording both signals together is challenging. To circumvent these challenges, specialised hardware and a range of signal processing methodologies are used to enable low-risk and high-fidelity recordings. EEG-fMRI is particularly valuable for applications where spontaneous brain activity, either physiological or pathological, is of interest. Spontaneous rhythmic activity has been studied since the start of EEG recordings, but EEG-fMRI has allowed us to view it in a new light. Importantly, in clinical neuroscience, combined EEG-fMRI has provided insights into epilepsy and sleep. Furthermore, it has also advanced our understanding of how EEG and fMRI signals relate to each other at a local and brain network scale. We summarise the current state of the art, how technical challenges have been met, and provide some examples of valuable insights made with EEG-fMRI in applications such as sleep and epilepsy.