Perylenetetracarboxylic diimides (PDIs) are among the most valuable functional dyes and have numerous potential applications. The structure modification of PDIs can be easily achieved at imide nitrogen atoms, bay positions, and ortho-positions, which makes PDIs with variable structures and properties. Applications as photo-functional and semiconducting materials have been intensively investigated in the past several decades. In the present review, general knowledge about PDI compounds, including various synthetic methods, and basic electronic and spectroscopic properties, are summarized. Recent progress in the research on covalently-linked PDI molecular arrays, including synthetic strategies and photophysical properties, is also discussed.