Integral operators play a key role in a wide range of mathematical models, including boundary integral formulations and nonlocal problems such as fractional differential equations. Their discretization by means of the boundary element method (BEM) or finite element techniques pose significant challenges due to singular kernels, nonlocal interactions, dense matrices, and reduced (boundary) regularity of solutions. Recently, many contributions to counteract these difficulties have been made that enable the accurate simulation of integral equations. The goal of this minisymposium is to bring together researchers currently working on the numerical analysis and implementation of boundary integral and fractional differential operators, with a particular focus on high-order methods and efficient discretizations such as adaptive mesh refinement, quadrature techniques, kernel approximation, and operator compression.