<p>Peatlands play an important role in the global methane (CH₄) cycle and models are key tools to assess global change effects on CH₄ processes. It remains unclear how well existing wetland modelling frameworks are suited to peatland questions. Therefore, we reviewed the published literature on 16 peatland and wetland models and reported spatial and temporal scales, spin-up periods for stabilization of different carbon pools, and various CH₄ production, oxidation and transport processes. Based on the information derived from the published literature, but without simulating any of the reviewed models and therefore without using a common assessment criterion, we summarized model benefits and challenges, common and unique model specific inputs, and inputs impacting CH₄ plant-mediated transport, diffusion and ebullition. Also, using the information derived from the published literature, the 16 reviewed models were distinguished into five categories with respect to varying degrees of process representation related to CH₄ production, oxidation and transport. We found the models that exhibited the full to adequate process representation regarding CH₄ production and oxidation are Ecosys, CLM-Microbe, ELM-Spruce, Peatland-VU, Wetland-DNDC, TEM-MDM, TRIPLEX-GHG, and CLM4Me. This literature review indicates that existing models are adequate for site-level CH₄ flux assessments, but their predictive power for CH₄ production, oxidation and transport processes remain unclear, until all reviewed models are simulated using a common assessment criterion. Overall, this review study provides a roadmap for selecting peatland and wetland models for early career researchers, first time/new modelers and non-expert modelers seeking literature published information on the available peatland and wetland models simulating CH₄ production, oxidation and transport processes.</p>