Extended discretization methods pose a number of new challenges to the designers and implementers of finite element software. Locally changing non-standard finite element spaces, implicit descriptions of domains boundaries, and polyhedral grid cells are just a short list of examples. The challenges drive thedesign of new codes and bring new ideas of how to construct simulation software. This minisymposium is intended to bring together experts on established as well as upcoming finite element codes that work on introducing X-DM ideas into their software.