In April 2012, a resolution was adopted for establishing "Intergovernmental science-policy Platform for Biodiversity and Ecosystem Services (IPBES)" as an independent intergovernmental body of United Nations (UN) according to the UN Office of Legal Affairs with the seat of the secretariat located in Bonn of Germany.IPBES has 136 members now and is continuously growing. China has formally joined IPBES after State Council of the People's Republic of China gave its stamp of approval in December of 2012. In order to guide the use of scenario analysis and modelling in all work under IPBES to ensure the policy relevance of its deliverables, 'the methodological assessment report on scenarios and models of biodiversity and ecosystem services' was firstly started up in early 2014, which was carried out by experts from all regions of the world. Its summary for policy-makers was approved by the fourth session of the Plenary of IPBES in February 2016 and has been launched in August 2016 in France. Nature, nature's contribution to people and driving forces of nature change are core concepts of the methodological assessment report. Nature includes biodiversity and ecosystems as well as earth system. Nature's contribution to people consists of ecosystem services and nature's gifts. Driving forces of nature change was classified into direct driving forces and indirect driving forces. Advanced work on scenarios and models of biodiversity and ecosystem services is one of deliverables of the work program up to 2030. We review background, history and contents of the scenarios and models of biodiversity and ecosystem services, describe the conceptual framework of IPBES scenarios include exploratory scenarios/attribution scenarios, policy-screening scenarios, target-seeking scenarios and retrospective policy evaluation, and discuss existing problems and perspectives for developing the models and scenarios. To find a solution for these existing problems on global level, a conceptual model is proposed for integrating dynamics of nature, changes of nature's contribution to people, and driving forces of the changes in terms of the fundamental theorem for Earth's surface system modeling. In the meanwhile, interactive mechanisms among nature, nature's contribution and driving forces are considered, along with combination of macro-pattern information and micro-process information.