The lecture introduces the ditance concept in graphs and some distance-related graph invariants. Emhasis will be given on the mean distance and the closely related Wiener index, the sum of distance between all pairs of vertices of graph. The examination of these graph invariants started 50 years ago, but is still an attractive topic of research. These indices are of considerable importance in computer science, network theory, chemistry, medicine, ... In the lecture some classical and some novel results are presented and the applications briefly outlined. Unsolved problems are pointed out.