Inspired by ongoing evolutions in the field of wireless body area networks (WBANs), this tutorial paper presents a conceptual and exploratory study of wireless electroencephalography (EEG) sensor networks (WESNs), with an emphasis on distributed signal processing aspects. A WESN is conceived as a modular neuromonitoring platform for high-density EEG recordings, in which each node is equipped with an electrode array, a signal processing unit, and facilities for wireless communication. We first address the advantages of such a modular approach, and we explain how distributed signal processing algorithms make WESNs more power-efficient, in particular by avoiding data centralization. We provide an overview of distributed signal processing algorithms that are potentially applicable in WESNs, and for illustration purposes, we also provide a more detailed case study of a distributed eye blink artifact removal algorithm. Finally, we study the power efficiency of these distributed algorithms in comparison to their centralized counterparts in which all the raw sensor signals are centralized in a near-end or far-end fusion center.