I will recall the Batalin-Vilkovisky formalism as interpreted by Costello and discuss several examples. The examples will be described using one take on (smooth) derived geometry. In computing the observable theory (after quantization) of these examples we will recover sheaves of twisted differential operators and also the algebraic index theorem of Fedosov and Nest-Tsygan. If time permits, I will discuss other examples coming from Lie algebroids and higher dimensional sigma models.