With data-centric network traffic growing exponentially between about 30% and 60% per year, fiber-optic transport networks are rapidly approaching their fundamental Shannon capacity limits. By 2020, leading-edge network operators will require capacities that are physically impossible to implement using conventional optical transmission technologies. We will explore key technology scaling disparities that are driving the looming capacity crunch in global core networks and discuss their impact on our communications society. We will then point to spatially parallel transmission solutions (Space-Division Multiplexing, SDM) as the only long-term viable solution to overcome the capacity scalability bottleneck. We will explore the implications of ultimately unavoidable spatial crosstalk, and examine how multiple-input-multiple-output (MIMO) digital signal processing well established in wireless communications, can help to scale optical core networks.