K. Binder, M. Müller, P. Virnau, L.G. MacDowell: Polymer+Solvent Systems: Phase Diagrams, Interface Free Energies, and Nucleation -- P.H. Hünenberger: Thermostat Algorithms for Molecular-Dynamics Simulations -- S. Auer, D. Frenkel: Numerical Simulation of Crystal Nucleation in Colloids -- D.R. Heine, G.S. Grest, J.G. Curro: Structure of Polymer Melts and Blends: Comparison of Integral Equation Theory and Computer Simulation.Soft matter science is nowadays an acronym for an increasingly important class of materials, which ranges from polymers, liquid crystals, colloids up to complex macromolecular assemblies, covering sizes from the nanoscale up the microscale. Computer simulations have proven as an indispensable, if not the most powerful, tool to understand properties of these materials and link theoretical models to experiments. In this first volume of a small series recognized leaders of the field review advanced topics and provide critical insight into the state-of-the-art methods and scientific questions of this lively domain of soft condensed matter research.