||This version of the review is a major update of the original article published in 2004. Two additional authors, Adam Pound and Ian Vega, have joined the article's original author, and each one has contributed a major piece of the update. The literature survey presented in Sections 2 was contributed by Ian Vega, and Part V (Sections 20 to 23) was contributed by Adam Pound. Part V replaces a section of the 2004 article in which the motion of a small black hole was derived by the method of matched asymptotic expansions; this material can still be found in Ref. , but Pound's work provides a much more satisfactory foundation for the gravitational self-force. The case study of Section 1.10 is new, and the ''exact'' formulation of the dynamics of a point mass in Section 19.1 is a major improvement from the original article. The concluding remarks of Section 24, contributed mostly by Adam Pound, are also updated from the 2004 article. The number of references has increased from 64 to 187.