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We survey results on the problem of covering the space ${\mathbb R}^n$, or aconvex body in it, by translates of a convex body. Our main goal is to presenta diverse set of methods. A theorem of Rogers is a central result, according towhich, for any convex body $K$, the space ${\mathbb R}^n$ can be covered bytranslates of $K$ with density around $n\ln n$. We outline four approaches toproving this result. Then, we discuss the illumination conjecture,decomposability of multiple coverings, Sudakov's inequality and some problemsconcerning coverings by sequences of sets.

Flavors of Translative Coverings