Neural networks, both in the human brain as well as artificial ones, show intriguing information processing capacities. Nonetheless, we lack a principled understanding how their functions emerge. A major challenge when assessing cortical processing lies in the subsampling problem: Despite rapid technological advances, we are still far from recording all neurons in an area with millisecond precision. Thus, one records either a subset of the neurons, or some spatial average of their activity, like LFP or EEG. We showed that such spatial subsampling can strongly bias inference about collective properties like clusters or neural avalanches. It even biases measures as basic as the correlation, thus any measure of effective connectivity or coupling between areas. We derived approaches to overcome the subsampling bias, and now have the toolset to make unbiased inferences. This has enabled us to revisit a long-standing debate about the nature of collective dynamics: Instead of the well-known asynchronous-irregular (AI) or critical dynamics, we find a novel, reverberating regime. Experimental evidence for that regime is now accumulating from cortical spike recordings in rat, cat, monkey and even human. The novel regime unifies a large body of contradictory, past results; it combines the advantages of the AI and critical state; and it enables each cortical circuit to tune its compute properties to task requirements by small adjustments of synaptic strength. Thereby each cortical circuit might be able to tune itself into the distributed computation of cortex in a flexible manner – and importantly also to tune-out if not needed.