We investigate the properties of systems on lattices with spatially distributed sensors and actuators. These systems arise in a variety of applications such as the control of vehicular platoons, formation of unmanned aerial vehicles, arrays of microcantilevers, and constellations of satellites. We use a Lyapunov-based framework as a tool for stabilization/regulation/asymptotic tracking of both linear and nonlinear systems. We first present results for nominal design and then describe the design of adaptive controllers in the presence of parametric uncertainties. These uncertainties are assumed to be temporally constant, but are allowed to be spatially varying. We show that, in most cases, the distributed design yields controllers with architecture similar to that of the original plant.