Résumé | The planar graphs have been, within decades of graph theory research, well explored yielding numerous results on their structural and chromatic properties. Along with this research, analogue problems were investigated for graphs which generalize - in various directions - the planar graphs. A particularly interesting generalization concerns the graph drawings in the plane which allow at most one crossing per edge, rising to the family of so called 1-planar graphs. These graphs, although introduced in late sixties of 20th century, were studied in a deeper detail only in the last decade. We survey known results on the global and local structure and chromaticity of 1-planar graphs with emphasis on similarities and fundamental differences when comparing with planar graphs, and several future research directions on an analogue of Steinberg conjecture for 1-planar graphs. |