I will overview the analytic classification of smooth, simple, 3-fold flops. There are three main aspects: (1) reducing the problem to the classification of certain noncommutative finite dimensional algebras, (2) a complete understanding of those algebras, then lastly (3) building the associated geometry for each algebra in that class. In the process of proving these results, we also obtain various bonus (and very surprising) geometric corollaries, including to curve-counting invariants, and also to 3-fold crepant divisor-to-curve contractions. Part (1) is joint with Joe Karmazyn and Emma Lepri, the rest is joint with Gavin Brown.