In the context of the anaerobic ammonium oxidation process (anammox), great scientific advances have been made over the past two decades, making anammox a consolidated technology widely used worldwide for nitrogen removal from wastewaters. This review provides a detailed and comprehensive description of the anammox process, the microorganisms involved and their metabolism. In addition, recent research on the application of the anammox process with alternative electron acceptors is described, highlighting the biochemical reactions involved, its advantages and potential applications for specific wastewaters. An updated description is also given of studies reporting the ability of microorganisms to couple the anammox process to extracellular electron transfer to insoluble electron acceptors; particularly iron, carbon-based materials and electrodes in bioelectrochemical systems (BES). The latter, also referred to as anodic anammox, is a promising strategy to combine the ammonium removal from wastewater with bioelectricity production, which is discussed here in terms of its efficiency, economic feasibility, and energetic aspects. Therefore, the information provided in this review is relevant for future applications.