Symplectic structures on Lie algebroids were introduced by Nest and Tsygan to extend Fedosov's work on deformation quantization to a wider class of Poisson manifolds, and by Martínez to develop a version of Lagrangian mechanics on Lie algebroids. I will give an overview of this area, including some joint work with Lin, Loizides, and Song about reduction and quantization of log symplectic manifolds.