Computation, synchronization, and measurement are key issues in complex networks. Vast nonlinear networks are encountered in biology, for instance, and in neuroscience, where for most tasks the human brain grossly outperforms engineered algorithms using computational elements 7 orders of magnitude slower than their artificial counterparts. We show that nonlinear dynamical systems analysis tools yield simple but highly non-intuitive insights about such issues, and that they also suggest systematic mechanisms to build progressively more refined networks and novel algorithms through stable accumulation of functional building blocks and motifs.