A pre-Dagstuhl reference (2014) is
Graph drawing beyond planarity: some results and open problems. G Liotta,ICTCS 14, 3-8 (2014).
The “beyond planarity” research area could be briefly described as the (potentially uncountable) collection of problems of the type depicted in the figure, where the column ”Forbidden” describes a forbidden crossing configuration and the column ”Question” describes a corresponding computational question of interest in graph drawing.