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This paper is devoted to Bertrand Russell’s criticism of Henri Bergson’s philosophy. It traces out the origins of that criticism and analyzes its essence, reasons and development in Russell’s works. Because of the importance of the concepts of space and time for Bergson’s philosophy and, in turn, the importance of continuity and discreteness for the understanding of space and time, the central part of the analysis concerns the views of both philosophers on continuity and discreteness, including Zeno’s paradoxes. The main thesis of the paper is that Russell’s criticism of Bergson’s philosophy comes, to a great extent, from Russell’s misunderstanding of Bergson.