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The pillars of modern physics, quantum mechanics and general relativity, coexist very successfully, having in their respective domains impressive observational support. However, questionable unification of the known forces, cosmological constant problems, black hole entropy puzzle, and conceptual difficulties of quantum mechanics and its application to the Universe are stumbling blocks on the way to a deeper understanding. - Attempts to quantize gravity continue to stimulate studies of classical and quantum dynamics and of statistical properties of "timeless" reparametrization-invariant systems. A central problem is to determine observables consistent with the constraints. New ideas attract attention that consider spacetime or gravity as emergent phenomena, much like hydrodynamics is seen to arise from atomic physics. Even quantum mechanics might reflect dynamics beneath, which is hidden by the coarse-graining to scales where quantum theory has been tested successfully, nineteen orders of magnitude away from the Planck scale. - Classical behavior in complex quantum systems, attributed to decoherence, has recently been studied from atomic to mesoscopic systems, the motivation being largely the quest for quantum information processing. However, decohering degrees of freedom in subatomic and general relativistic systems are little understood. The control of quantum systems by classical means and the study of quantum-classical hybrid dynamics present new challenges of practical as well as of fundamental character. The related measurement problem, wave function collapse or objective reduction persist as unresolved issues. - The study of these topics may include an analysis of the kind of information that exists in systems with many degrees of freedom and typically long-range interactions and of the basic conditions under which it can be extracted. Corresponding measures of complexity have been elaborated and could play a role here.