The aim of this minisymposium is to discuss and to share recent advances regarding mathematical modelling, numerical discretization and solution techniques, computational algorithms and software optimization, validation and benchmarking configurations and high performance computing simulations in the case of real-life applications for the efficient treatment of viscoelastic flow problems. Typical topics may cover new ideas regarding numerical techniques for a broad range of Weissenberg numbers, but also new approaches w.r.t. differential and integral models to describe the complex rheological behaviour, up to future high performance computing environments which will be in the exascale range and which will include massively parallel, heterogeneous architectures together with specific accelerator hardware (GPUs) including reduced arithmetic precision, are in the focus of this minisymposium. The minisymposium will mainly concentrate on methods and their foundations, and will highlight the interplay of these aspects with computational and algorithmic tools and particularly their realization in software to address current and future challenges in the field.