  This is a survey article on recent progress of comparison geometry and
geometric analysis on Finsler manifolds of weighted Ricci curvature bounded
below. Our purpose is two-fold: Give a concise and geometric review on the
birth of weighted Ricci curvature and its applications; Explain recent results
from a nonlinear analogue of the $\Gamma$-calculus based on the Bochner
inequality. In the latter we discuss some gradient estimates, functional
inequalities, and isoperimetric inequalities.
