The vortex filament model has become a standard and powerful tool to visualize the motion of quantized vortices in helium superfluids. In this article, we present an overview of the method and highlight its impact in aiding our understanding of quantum turbulence, particularly superfluid helium. We present an analysis of the structure and arrangement of quantized vortices. Our results are in agreement with previous studies showing that under certain conditions, vortices form coherent bundles, which allows for classical vortex stretching, giving quantum turbulence a classical nature. We also offer an explanation for the differences between the observed properties of counterflow and pure superflow turbulence in a pipe. Finally, we suggest a mechanism for the generation of coherent structures in the presence of normal fluid shear.