  Distance matrices of graphs were introduced by Graham and Pollack in 1971 to
study a problem in communications. Since then, there has been extensive
research on the distance matrices of graphs -- a 2014 survey by Aouchiche and
Hansen on spectra of distance matrices of graphs lists more than 150
references. In the last ten years, variants such as the distance Laplacian, the
distance signless Laplacian, and the normalized distance Laplacian matrix of a
graph have been studied. After a brief description of the early history of the
distance matrix and its motivating problem, this survey focuses on comparing
and contrasting techniques and results for the four types of distance matrices.
Digraphs are treated separately after the discussion of graphs, including
discussion of similarities and differences between graphs and digraphs. New
results are presented that complement existing results, including results for
some the matrices on unimodality of characteristic polynomials for graphs,
preservation of parameters by cospectrality for graphs, and bounds on spectral
radii for digraphs.
