The Multi-Compartment Hg (mercury) Modeling and Analysis Project (MCHgMAP) is an international multimodel research initiative intended to simulate and analyze the geospatial distributions and temporal trends of environmental Hg to inform effectiveness evaluations of two multilateral environmental agreements (MEAs): the Minamata Convention on Mercury (MC) and the Convention on Long-Range Transboundary Air Pollution (LRTAP). This MCHgMAP overview paper presents its science objectives, background, and rationale; experimental design (multimodel ensemble (MME) architecture, inputs and evaluation data, simulations, and reporting framework); and methodologies for the evaluation and analysis of simulated environmental Hg levels. The primary goals of the project are to facilitate detection and attribution of recent (observed) and future (projected) spatial patterns and temporal trends of global environmental Hg levels and identification of key knowledge gaps in Hg science and modeling to improve future effectiveness evaluation cycles of the MEAs. The current advances and challenges of Hg models, emission inventories, and observational data are examined, and an optimized multimodel experimental design is introduced to address the key policy questions of the MEAs. A common set of emissions, environmental conditions, and observation datasets is proposed (where possible) to enhance the MME comparability. A novel harmonized simulation approach between atmospheric, land, oceanic, and multimedia models is proposed to account for the short- and long-term changes in secondary Hg exchanges and to achieve mechanistic consistency of Hg levels across environmental matrices. A comprehensive set of model experiments is proposed and prioritized to ensure systematic analysis and participation of a variety of models from the scientific community.