Modelling decoherence in quantum spin systems

In this review we discuss approaches to numerical modelling of decoherence by a spin bath. We consider several popular simulation methods, briefly discussing their implementation, and analyse their advantages and drawbacks. Furthermore, we consider application of these methods to several different physical systems, demonstrating how the numerical simulations can help in understanding the details of the decoherence process in quantum spin systems. The discussion of possible interesting directions for further research concludes the review. (topical review)