Thurston's Geometrization Conjecture is a theory proposed by mathematician William Thurston in the 1970s. It suggests that every three-dimensional manifold can be decomposed into pieces that each have one of eight distinct geometric structures. This conjecture extends the ideas of topology and geometry to classify and understand the shapes of three-dimensional spaces. The conjecture was proven for all closed, orientable three-manifolds by Grigori Perelman in the early 2000s, using techniques from Ricci flow. This breakthrough not only confirmed Thurston's ideas but also significantly advanced the field of geometric topology, influencing how mathematicians study the properties of three-dimensional spaces.