Anaerobic digestion of animal manure results in the production of renewable energy (biogas) and nutrient-rich biofertilizer. A further benefit of the technology is decreased greenhouse gas emissions that otherwise occur during manure storage. Since animal manure makes anaerobic digestion cost-efficient and further advance the technology for higher methane yields, it is of utmost importance to find strategies to improve bottlenecks such as the degradation of lignocellulose, e.g., in cattle manure, or to circumvent microbial inhibition by ammonia caused by the degradation of nitrogen compounds in, e.g., chicken, duck, or swine manure. This review summarizes the characteristics of different animal manures and provides insight into the underlying microbial mechanisms causing challenging problems with the anaerobic digestion process. A particular focus is put upon the retention time and organic loading rate in high-ammonia processes, which should be designed and optimized to support the microorganisms that tolerate high ammonia conditions, such as the syntrophic acetate oxidizing bacteria and the hydrogenotrophic methanogens. Furthermore, operating managements used to stabilize and increase the methane yield of animal manure, including supporting materials, the addition of trace elements, or the incorporation of ammonia removal technologies, are summarized. The review is finalized with a discussion of the research needed to outline conceivable operational methods for the anaerobic digestion process of animal manure to circumvent process instability and improve the process performance.