Anaerobic bioprocesses, such as anaerobic digestion and dark fermentation, provide energy carriers in the form of methane and hydrogen gases, respectively. However, their wastewater-type residues, that is, the fermentation effluents, must be treated carefully due to the incomplete and non-selective conversion of organic matter fed to the actual system. For these reasons, the effluents contain various secondary metabolites and unutilized substrate, in most cases. Only a fraction of anaerobic effluents can be directly applied for fertilization under a moderate climate. Conventional wastewater treatment technologies may be used to clean the remainder, but that approach leads to a net loss of energy and of potentially useful agricultural input materials (organic carbon and NPK fertilizer substitutes). The rationale of this paper is to provide an overview of promising new research results in anaerobic effluent management strategies as a part of technological downstream that could fit the concept of new-generation biorefinery schemes aiming towards zero-waste discharge, while keeping in mind environmental protection, as well as economical perspectives. According to the literature, the effluents of the two above processes can be treated and valorized relying either on membrane bioreactors (in case of anaerobic digestion) or bio-electrochemical apparatus (for dark fermentation). In this work, relevant findings in the literature will be reviewed and analyzed to demonstrate the possibilities, challenges, and useful technical suggestions for realizing enhanced anaerobic effluent management. Both membrane technology and bio-electrochemical systems have the potential to improve the quality of anaerobic effluents, either separately or in combination as an integrated system.