Multiscale Discontinuous Galerkin Methods for Elliptic Problems with Multiple Scales -- Discrete Network Approximation for Highly-Packed Composites with Irregular Geometry in Three Dimensions -- Adaptive Monte Carlo Algorithms for Stopped Diffusion -- The Heterogeneous Multi-Scale Method for Homogenization Problems -- A Coarsening Multigrid Method for Flow in Heterogeneous Porous Media -- On the Modeling of Small Geometric Features in Computational Electromagnetics -- Coupling PDEs and SDEs: The Illustrative Example of the Multiscale Simulation of Viscoelastic Flows -- Adaptive Submodeling for Linear Elasticity Problems with Multiscale Geometric Features -- Adaptive Variational Multiscale Methods Based on A Posteriori Error Estimation: Duality Techniques for Elliptic Problems -- Multipole Solution of Electromagnetic Scattering Problems with Many, Parameter Dependent Incident Waves -- to Normal Multiresolution Approximation -- Combining the Gap-Tooth Scheme with Projective Integration: Patch Dynamics -- Multiple Time Scale Numerical Methods for the Inverted Pendulum Problem -- Multiscale Homogenization of the Navier-Stokes Equation -- Numerical Simulations of the Dynamics of Fiber Suspensions.Multiscale problems naturally pose severe challenges for computational science and engineering. The smaller scales must be well resolved over the range of the larger scales. Challenging multiscale problems are very common and are found in e.g. materials science, fluid mechanics, electrical and mechanical engineering. Homogenization, subgrid modelling, heterogeneous multiscale methods, multigrid, multipole, and adaptive algorithms are examples of methods to tackle these problems. This volume is an overview of current mathematical and computational methods for problems with multiple scales with applications in chemistry, physics and engineering.