5421 eng reportzib 0 -- 2015-03-27 -- Markov State Modelling as a concept for a coarse grained description of the essential kinetics of a molecular system in equilibrium has gained a lot of atten- tion recently. The last 10 years have seen an ever increasing publication activity on how to construct Markov State Models (MSMs) for very different molecular systems ranging from peptides to proteins, from RNA to DNA, and via molecu- lar sensors to molecular aggregation. Simultaneously the accompanying theory behind MSM building and approximation quality has been developed well be- yond the concepts and ideas used in practical applications. This article reviews the main theoretical results, provides links to crucial new developments, outlines the full power of MSM building today, and discusses the essential limitations still to overcome. 10.1140/epjst/e2015-02421-0 urn:nbn:de:0297-zib-54218 1438-0064 appeared in: The European Physical Journal Special Topics Christof Schütte Erlinda Körnig Marco Sarich 15-18 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40] Biophysics Numerical Mathematics Schütte, Christof SFB-1114-B3 https://opus4.kobv.de/opus4-zib/files/5421/ZIB-Report_15-18.pdf