The last two decades have brought us a tremendous improvement in numerical methods, and the field of computer simulations has been established as the third pillar used to increase our knowledge of natural science. As such it is of equal importance as experiments and theory in sharpening our understanding of the complex real world phenomena. It is undeniable that the increase in computer power experienced in the last two decades has enormously contributed to boost simulations. One one hand, as the computer power increases so does the ambition of the researchers to describe even more complex systems which involve large differences in the spatial and time scales of their components. On the other hand, it is also clear that brute force alone will not pave the way to solving those issues. In the last decade the introduction of smart algorithms have been more profitable to science than the simple improvements in turn of pure CPU power. Therefore there is still an urgent and constant need for more efficient and clever algorithms, as well as for improved theoretical frameworks. Such achievements are of great interest for the scientific community as a whole, but here in this special issue we would like to highlight achievements and novel simulation approaches to certain areas of polymeric and soft matter systems.Soft matter, also sometimes denoted as complex fluids, is inherently more difficult to deal with than simple, molecular fluids. Soft matter systems can consist of colloidal, polymeric systems, but also biological systems like blood, DNA, tissues, biological cells, or even bacterial colonies. Their structure shows more complex behavior, and the involved time and length scales are orders of magnitude larger that can even reach glassy behaviour. These systems therefore show a clear urge for efficient sampling techniques, or even the necessity to reduce the degrees of freedom by some coarse-graining strategy in order to reach the necessary length and time scales fort he problem under consideration. However, often it is not obvious to decide which degrees of freedom can be safely averaged over, and which ones one should keep. The