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In recent years the interaction between geometric topology and classical and quantum field theories has attracted a great deal of attention from both the mathematicians and physicists. This interaction has been especially fruitful in low dimensional topology. In this article We discuss some topics from the geometric topology of 3-manifolds with or without links where this has led to new viewpoints as well as new results. They include in addition to the early work of Witten, Casson, Bott, Taubes and others, the categorification of knot polynomials by Khovanov. Rozansky, Bar-Natan and Garofouladis and a special case of the gauge theory to string theory correspondence {in the Euclidean version of the theories,} where exact results are available. We show how the Witten-Reshetikhin-Turaev invariant in