In the past 40+ years there have been many revolutions in knot theory and 3-manifold topology. Three of the main successful approaches have been due to the work of Thurston (the Geometrization Conjecture), Vaughan Jones (the Jones polynomial), and Simon Donaldson (Donaldson invariants and Floer homology). We will summarize some of these topics and the role that MSRI/SLMath has played in their development. Then we will indicate the prospects for discovering connections between these subjects, such as the Volume Conjecture and the L-Space Conjecture.