Abstract: The classical de Rham-Hodge theory implies that each cohomology class of a compact manifold is uniquely represented by a harmonic form, signifying the important role of Laplacian in geometry. The talk aims to explain some results concerning the size and structure of its spectrum. After a brief overview for both bounded Euclidean domains and compact manifolds, we focus on complete Riemannian manifolds. Our emphasis is on sharp estimates and rigidity of the bottom spectrum in terms of Ricci or scalar curvature lower bound.