A theorem of Chris Wendl allows you to completely characterize symplectic fillings of genus 0 open book decompositions by factorizations of their monodromy into Dehn twists. Olga Plamenevskaya and I use this to generalize results of Eliashberg, McDuff and Lisca to classify the fillings of certain Lens spaces. I'll discuss this and a newer version of Wendl's theorem, joint with Wendl and Sam Lisi, this time for spinal open books, as well as some applications: obstructions to symplectic fillings, classification of fillings, and contact manifolds with infinitely many fillings.