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Topological K-theory is one of the most important invariants for noncommutative algebras equipped with a suitable topology or bornology. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory.We describe a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, we discuss other approaches to bivariant K-theories for operator algebras.