Fibrillar adhesive structures are important for several natural and technical applications; these include both the adhesion mechanism of several insects or lizards and the fabrication of bio-inspired adhesives. The underlying mechanisms are characterized by a particular hierarchical microstructure of branching hairs, spanning multiple length scales. Studying the adhesion behavior of fibrillar adhesives, we present a multiscale modeling approach that is based on five modeling levels. Starting with the finest length scale, we consider 1) an atomistic description of van der Waals adhesion, 2) an effective continuum contact model capturing both normal and tangential contact, 3) a detailed continuum finite element (FE) model for the adhesive fibril tips, 4) a reduced tip model based on a nonlinear beam FE formulation, and 5) a global beam FE model for the entire fibril. Adaptive mesh refinement techniques are used both to increase efficiency and to model peeling accurately. As a computational example, we discuss the hierarchical structure of a gecko seta. The proposed modeling approach is general, and readily carries over to other fibrillar adhesives.