A Besicovitch set is a compact set in R^d that contains a unit line segment pointing in every direction. The Kakeya conjecture asserts that every Besicovitch set in R^d must have Hausdorff dimension d. I will discuss a recent improvement on the Kakeya conjecture in three dimensions, which says that every Kakeya set in R^3 must have Hausdorff dimension at least 5/2 + \eps, where \eps is a small positive constant. This is joint work with Nets Katz

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