I will review some aspects of my recent research in different areas. First, I will present several limit theorems for Brownian winding functionals on some Riemannian symmetric spaces and special Lie groups of matrices. Then, I will turn to some results in the study of Ricci curvature bounds in sub-Riemannian geometry. Finally, I will explain some recent developments in the study of Sobolev spaces on rough metric measure spaces like nested fractals.