The Menger and Rothberger covering properties, and their formulations as selection principles, have been well-studied in the past few decades. In 2010, Aurichi showed (using a pair of topological games) that each Menger space is also a D-space, giving a partial answer to a long-standing question by Van Douwen. Interest in "weakened" versions of the covering properties has increased in the years since.

We will present a brief survey of the Menger property and its cousins, and its characterizations as a selection principle and a topological game.