  We investigate the problem of drawing graphs in 2D and 3D such that their
edges (or only their vertices) can be covered by few lines or planes. We insist
on straight-line edges and crossing-free drawings. This problem has many
connections to other challenging graph-drawing problems such as small-area or
small-volume drawings, layered or track drawings, and drawing graphs with low
visual complexity. While some facts about our problem are implicit in previous
work, this is the first treatment of the problem in its full generality. Our
contribution is as follows.
  We show lower and upper bounds for the numbers of lines and planes needed for
covering drawings of graphs in certain graph classes. In some cases our bounds
are asymptotically tight; in some cases we are able to determine exact values.
  We relate our parameters to standard combinatorial characteristics of graphs
(such as the chromatic number, treewidth, maximum degree, or arboricity) and to
parameters that have been studied in graph drawing (such as the track number or
the number of segments appearing in a drawing).
  We pay special attention to planar graphs. For example, we show that there
are planar graphs that can be drawn in 3-space on a lot fewer lines than in the
plane.
