This article provides a very general survey on some aspects of topological quantum field theory. Apparently, it is the written version of a talk that the author has delivered to a wider audience of mathematicians and physicists. The main subject of this survey is a special topic in string theory, namely the recently developed theory of (so-called) \(B\)-fields. The string theory associated with a space-time \(X\) is closely related to the loop space \({\mathfrak L}X\) of \(X\), and a \(B\)-field on \(X\) is defined to be a complex Hermitian line bundle on the loop space \({\mathfrak L}X\), equipped with a certain family of tensorial operators which form a so-called string connection. The author describes the geometric structure of such a B-field (also called a ``gerbe with connection''), illustrates its relationship with noncommutative geometry, and explains a way how to use a \(B\)-field to define a twisted version of the (topological) \(K\)-theory of the underlying space-time. This includes a discussion of the so-called string backgrounds, within conformal quantum field theory, as well as a \(K\)-theoretic interpretation of the D-branes of the according field theory resulting from this approach. Basically, this highly enlightening and inspring survey reflects some new ideas in topological quantum field theory, which come from the author's joint work with M. F. Atiyah and G. Moore in this fascinating, rather recent field of research in mathematical physics.