A surprisingly consistent view on the fundamental nature of complex systems can now be drawn from the convergence of three distinct research themes. First, molecular biology has provided a detailed description of much of the components of biological networks, and the organizational principles of these networks are becoming increasingly apparent. It is now clear that much of the complexity in biology is driven by its regulatory networks, however poorly understood the details remain. Second, advanced technology is creating engineering examples of networks with complexity approaching that of biology, where we do know all the details. While the components are entirely different, there is striking convergence at the network level of the architecture and the role of protocols, layering, control, and feedback in structuring complex system modularity. Finally, there is a new mathematical framework for the study of complex networks that suggests that this apparent network-level evolutionary convergence both within biology and between biology and technology is not accidental, and follows necessarily from the requirements that both biology and technology be efficient, robust, adaptive, and evolvable. A crucial insight is that both evolution and natural selection or engineering design must produce high robustness to uncertain environments and components in order for systems to persist. Yet this allows and even facilitates severe fragility to novel perturbations, particularly those that exploit the very mechanisms providing robustness, and this "robust yet fragile'" (RYF) feature must be exploited explicitly in any theory that hopes to scale to large systems. This talk will focus on how the above views of "organized complexity" contrast sharply with the view of "emergent complexity" that is popular among physicists. While motivation will be drawn from biology and technology, greater emphasis will be on the model systems and phenomena, such as lattices, cellular automata, spin glasses, phase transitions, criticality, chaos, fractals, scale-free networks, self-organization, and so on, that have been the inspiration for the physics perspective. This has several potential benefits. One is that it seems to offer a novel way of teaching concepts and mathematics of organized complexity to a much broader audience while deferring the high level of domain detail currently necessary to understand the model systems from biological or technological networks. Another is that it provides apparently novel insights into RYF aspects of longstanding mysteries in physics, from coherent structures in shear flow turbulence and coupled oscillators, to the ubiquity of power laws, to the nature of quantum entanglement, to the origin of dissipation. Finally, the underlying mathematics may offer new tools to explore other problems in physics where RYF features may play a role, particularly involving multiple scales and organized structures and phenomena.