The electroencephalogram (EEG) is a classic noninvasive method for measuring a person's brain waves and is used in a large number of fields: from epilepsy and sleep disorder diagnosis to brain-computer interfaces (BCIs). Electrodes are placed on the scalp to detect the microvolt-sized signals that result from synchronized neuronal activity within the brain. Current long-term EEG monitoring is generally either carried out as an inpatient in combination with video recording and long cables to an amplifier and recording unit or is ambulatory. In the latter, the EEG recorder is portable but bulky, and in principle, the subject can go about their normal daily life during the recording. In practice, however, this is rarely the case. It is quite common for people undergoing ambulatory EEG monitoring to take time off work and stay at home rather than be seen in public with such a device. Wearable EEG is envisioned as the evolution of ambulatory EEG units from the bulky, limited lifetime devices available today to small devices present only on the head that can record EEG for days, weeks, or months at a time. Such miniaturized units could enable prolonged monitoring of chronic conditions such as epilepsy and greatly improve the end-user acceptance of BCI systems. In this article, we aim to provide a review and overview of wearable EEG technology, answering the questions: What is it, why is it needed, and what does it entail? We first investigate the requirements of portable EEG systems and then link these to the core applications of wearable EEG technology: epilepsy diagnosis, sleep disorder diagnosis, and BCIs. As a part of our review, we asked 21 neurologists (as a key user group) for their views on wearable EEG. This group highlighted that wearable EEG will be an essential future tool. Our descriptions here will focus mainly on epilepsy and the medical applications of wearable EEG, as this is the historical background of the EEG, our area of expertise, and a core motivating area in itself, but we will also discuss the other application areas. We continue by considering the forthcoming research challenges, principally new electrode technology and lower power electronics, and we outline our approach for dealing with the electronic power issues. We believe that the optimal approach to realizing wearable EEG technology is not to optimize any one part but to find the best set of tradeoffs at both the system and implementation level. In this article, we discuss two of these tradeoffs in detail: investigating the online compression of EEG data to reduce the system power consumption and the optimal method for providing this data compression.