Anaerobic digestion (AD) is a well-established technology used for producing biogas or biomethane alongside the slurry used as biofertilizer. However, using a variety of wastes and residuals as substrate and mixed cultures in the bioreactor makes AD as one of the most complicated biochemical processes employing hydrolytic, acidogenic, hydrogen-producing, acetate-forming bacteria as well as acetoclastic and hydrogenoclastic methanogens. Hydrogen and volatile fatty acids (VFAs) including acetic, propionic, isobutyric, butyric, isovaleric, valeric and caproic acid and other carboxylic acids such as succinic and lactic acids are formed as intermediate products. As these acids are important precursors for various industries as mixed or purified chemicals, the AD process can be bioengineered to produce VFAs alongside hydrogen and therefore biogas plants can become biorefineries. The current review paper provides the theory and means to produce and accumulate VFAs and hydrogen, inhibit their conversion to methane and to extract them as the final products. The effects of pretreatment, pH, temperature, hydraulic retention time (HRT), organic loading rate (OLR), chemical methane inhibitions, and heat shocking of the inoculum on VFAs accumulation, hydrogen production, VFAs composition, and the microbial community were discussed. Furthermore, this paper highlights the possible techniques for recovery of VFAs from the fermentation media in order to minimize product inhibition as well as to supply the carboxylates for downstream procedures.