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This paper gives an introduction to Kuga-Satake varieties and discusses someaspects of the Hodge conjecture related to them. Kuga-Satake varieties areabelian varieties associated to certain weight two Hodge structures, forexample the second cohomology group of a K3 surface. We give a detailed accountof the construction of Kuga-Satake varieties and of their decomposition insimple subvarieties. We recall the Hodge conjecture and we point out aconnection between the Hodge conjecture for abelian fourfolds and Kuga-Satakevarieties. We discuss the implications of the Hodge conjecture on the geometryof surfaces whose second cohomology group has a Kuga-Satake variety. Weconclude with some recent results on Kuga-Satake varieties of Hodge structureson which an imaginary quadratic field acts.

Kuga-Satake Varieties and the Hodge Conjecture