Fractional diffusion is a common way to model anomalous diffusion, where the assumption of Brownian motion of particles does not hold. This talk focuses on the so-called integral fractional Laplacian and related fractional-order operators on bounded domains. The aim of the talk is to provide students a basic understanding of the research in this area. We shall first present the definition of integral fractional Laplacian and the regularity theories in the literature. We will then discuss several numerical methods for fractional Laplacian including the classical conforming finite element discretizations on graded meshes and the approach based on the Dunford-Taylor representation. Moreover, we will also consider some nonlinear fractional problems such as nonlocal minimal surfaces and fractional p-Laplacian.