The indiscriminate release of significant amounts of food waste, fat oil and grease, and sewage sludge (SS) into the environment causes severe contamination in many nations. There are numerous potential treatment methods to cope with organic wastes, but anaerobic digestion is currently widely accepted to handle different kinds of biological waste. One of the pillars supporting anaerobic digester biogas production increase in treatment plants is the use of fats in the wastewater. However, it has been claimed that high-fat wastes, particularly mono-digestion in the anaerobic reactor, inhibit acetoclastic and methanotrophic bacteria delay the formation of gas even more, and overtax the system. The aim of this review is to review several publications that dealt with the effect of LCFs and FOG on AD performance and associated methane production and microbial communities, as well as the mechanism of LCFA generation and its inhibitory effect on anaerobic digestion performance, and also addressed the improvement of system efficiency using co-digestion with lipid wastes.