  We classify various types of graded extensions of a finite braided tensor
category $\cal B$ in terms of its $2$-categorical Picard groups. In particular,
we prove that braided extensions of $\cal B$ by a finite group $A$ correspond
to braided monoidal $2$-functors from $A$ to the braided $2$-categorical Picard
group of $\cal B$ (consisting of invertible central $\cal B$-module
categories). Such functors can be expressed in terms of the Eilnberg-Mac~Lane
cohomology. We describe in detail braided $2$-categorical Picard groups of
symmetric fusion categories and of pointed braided fusion categories.
