Abstract: It is of general interest to study the difference between Ricci and sectional curvature lower bound. A well known difference is their control on Betti numbers. Recently, joint with J. Pan, we constructed manifolds/singular spaces with nonnegative Ricci curvature which give negative answers to two long open questions. One is about the properness of Busemann functions, and the other one regards the singular set of Ricci limit sets. Building on these, very recently, joint with X. Dai, S. Honda, J. Pan, we discover two surprising types of Weyl's laws which are fractal-like for some compact singular space with "Ricci lower bound" (Ricci limit spaces). These show dramatic new features for Ricci lower bound.