The analysis of large-scale networked systems is one of the most interesting current challenges in dynamical systems. In this talk, I will present a perspective on this problem that combines an operator-theoretic and graph-theoretic approach, but also incorporates, in a strong way, the geometric point of view that is so fruitful in low dimensions. This approach leads to a new proposal for model reduction that is rooted in the dynamics of the system rather than in energy-minimization arguments. It also enables analysis of uncertain and stochastic systemswhere initial conditions and/or parameter values are not known exactlywithin the same framework. Most of the tools apply equally to discontinuous systems. I will motivate the approach by a number of examples, ranging from biomolecular models to power grid systems, that exhibit large-scale (emergent) transitions between states.