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In its purest form, Bondi-Hoyle-Lyttleton accretion concerns the supersonic motion of a point mass through a gas cloud. The cloud is assumed to be free of self-gravity, and to be uniform at infinity. Gravity focuses material behind the point mass, which can then accrete some of the gas. This problem has found applications in many areas of astronomy, and this paper is an attempt to address the lack of a general review of the subject.

I start with a short summary of the original work of Bondi, Hoyle and Lyttleton, followed by a discussion of the numerical simulations performed. Some issues in Bondi-Hoyle-Lyttleton accretion are discussed, before a brief summary of the fields in which the geometry has proved useful.