Over the last two decades, increasing efforts have been devoted by numerous researchers in a wide range of fields to design new composite materials with enhanced coupled properties. Most of these efforts have focused on soft organic materials because of their potential to undergo large reversible deformations when subjected to a variety of external stimuli, such as electric and magnetic fields, temperature changes and chemical changes. The focus of this course will be on the electro- and magneto-mechanics of soft composite materials and structures. These may comprise hierarchical microstructures and/or micro-architectures spanning several length scales from the nano- to the centi-meter. The focus of the course will be on magnetorheological elastomers (MREs) and dielectric elastomer composites (DECs), which are composite materials that comprise ferromagnetic and high-dielectric/conducting filler nano- and micro-particles embedded in a soft polymeric matrix. This gives rise to a coupled magneto- and electro-mechanical response at the macroscopic (order of millimeters and larger) scale when they are subjected to magneto- electro-mechanical external stimuli. While such MRE and DEC materials and devices can become unstable at some critical electro-magneto-mechanical loading, their response may be well controlled in the post-instability regime. This feature motivates the operation of these devices in this unstable region to obtain controlled pattern formation, soft robotic motion and artificial muscles, controllable band-gap acoustic and electromagnetic properties, energy harvesting as well as actively controlled stiffness (for cell-growth). The topics of this Advanced School will include the presentation of experimental fabrication and testing techniques for MREs and DECs, the derivation of thermodynamically-consistent coupled variational formulations, the numerical implementation and analysis of MREs and DECs as well as of their stability using homogenization techniques, theoretical coupled homogenization and phenomenological continuum theories. The course will emphasize the significance of an integrated experimental-analytical-numerical approach across the relevant length scales. The Course will consist of introductory lectures on the theoretical aspects of such materials, followed by lectures on more specialized topics given by eminent experts in the field of experiments, phenomenological and micromechanical modeling of active composites and structures, instabilities and energy harvesting. The course will close with recent examples showing the necessary but also powerful combination of experiments, numerics and theory to study the response of MREs and DECs and their instabilities. The School is addressed to doctoral students, post-docs and early career researchers with interest in active soft materials. The course is designed to give an integrated experimental, numerical and theoretical viewpoint on such novel material systems as well as possible future research directions in this field.