The fight against climate change requires consideration of carbon as a critical parameter in production systems, with the ultimate aim of creating a truly sustainable circular carbon economy. In this context, microbial bioproduction systems are a promising route to renewably generate value-added chemicals and fuels. Methanol and formate have recently gained interest as microbial one-carbon feedstocks, which can be produced sustainably from carbon dioxide and renewable energy, are easy to store and transport and readily dissolve in aqueous solutions. Acetogenic bacteria are strictly anaerobic microorganisms that can grow autotrophically on molecular hydrogen or use methanol, formate, and carbon monoxide as their sole carbon and energy sources via the Wood-Ljungdahl pathway, the most energetically efficient carbon fixation pathway known to date. Here, known variants of the Wood-Ljungdahl pathway, the physiology of a selection of methylotrophic and formatotrophic acetogens, and emphasize recent advancements in bioprocessing with respect to quantification of acetogen metabolism of methanol and formate as well as research aiming at establishing novel bioprocesses are reviewed. Additionally, the tools available for physiological and metabolic studies as well as for metabolic and genetic engineering are discussed. Finally, the features and constraints that govern the bioenergetics and stoichiometry of acetogen metabolism during growth on methanol and formate are reviewed, and future perspectives of the field discussed. The high energetic efficiency with which acetogens can convert methanol and formate into products renders them highly attractive platform hosts in the circular carbon economy.