  Some results on cross-diffusion systems with entropy structure are reviewed.
The focus is on local-in-time existence results for general systems with
normally elliptic diffusion operators, due to Amann, and global-in-time
existence theorems by Lepoutre, Moussa, and co-workers for cross-diffusion
systems with an additional Laplace structure. The boundedness-by-entropy method
allows for global bounded weak solutions to certain diffusion systems.
Furthermore, a partial result on the uniqueness of weak solutions is recalled,
and some open problems are presented.
