In 1995 the Fraunhofer Institute for Industrial Mathematics started a research project in order to simulate the paper transport in a printing machine. The transport of papers in printing machines can be modelled as two-dimensional fluid-structure interaction problem. The equations describing the dynamics of the paper transport are derived from shell models based on continuum mechanics that are equivalent to rod models for fiber dynamics. In order to simulate nonwoven production processes the Fraunhofer Institute for Industrial Mathematics extended the Cosserat rod models by a stochastic drag model for fibers in turbulent flows. FIDYST demonstrated its proof of concept 2007. At the EDANA Symposium 2007 the industrial company Oerlikon Neumag presented a new pilot plant where FIDYST had successfully been applied to increase the tenacity of the produced nonwoven. In 2012 the software code was ported from C to C++. 2014 the interaction of fibers with machinery parts was introduced in FIDYST. The latest release of FIDYST can simulate staple fibers.