Studies of global environmental change make extensive use of scenarios to explore how the future can evolve under a consistent set of assumptions. The recently developed Shared Socioeconomic Pathways (SSPs) create a framework for the study of climate-related scenario outcomes. Their five narratives span a wide range of worlds that vary in their challenges for climate change mitigation and adaptation. Here we provide background on the quantification that has been selected to serve as the reference, or ‘marker’, implementation for SSP2. The SSP2 narrative describes a middle-of-the-road development in the mitigation and adaptation challenges space. We explain how the narrative has been translated into quantitative assumptions in the IIASA Integrated Assessment Modelling Framework. We show that our SSP2 marker implementation occupies a central position for key metrics along the mitigation and adaptation challenge dimensions. For many dimensions the SSP2 marker implementation also reflects an extension of the historical experience, particularly in terms of carbon and energy intensity improvements in its baseline. This leads to a steady emissions increase over the 21st century, with projected end-of-century warming nearing 4 °C relative to preindustrial levels. On the other hand, SSP2 also shows that global-mean temperature increase can be limited to below 2 °C, pending stringent climate policies throughout the world. The added value of the SSP2 marker implementation for the wider scientific community is that it can serve as a starting point to further explore integrated solutions for achieving multiple societal objectives in light of the climate adaptation and mitigation challenges that society could face over the 21st century.