Neurons in the brain have tight anatomical connections through dendritic arborizations that integrate diverse inputs and axons that project outputs to multiple, distributed areas. How do individual neurons or regions reorganize their activity so that they selectively process particular inputs and direct their outputs to match the timescale of behaviors? In this work, we show that large-scale cortical “traveling waves” underlie this rapid and selective reorganization, by propagating in specific directions, thus flexibly and efficiently communicating between the given brain regions. We designed a novel, flexible analytical framework for measuring general patterns of traveling wave propagation during human cognition, and applied this procedure to direct brain recordings from neurosurgical patients performing multiple memory experiments. In previous work, traveling waves were shown to play a critical role for certain behaviors such as visual processing and spatial navigation in rodents (Lubenov \& Siapas, 2009, Nature) and non-human primates (Davis et al., 2020, Nature), and recently in human cognition (Zhang et al., 2018, Neuron; Mohan et al., 2024, Nature Human Behavior), however, these waves were planar waves, severely limiting their ability to rapidly and dynamically reorganize to adapt to complex behaviors in humans. Our results showed an array of complex traveling wave propagation patterns including sources, sinks, spirals, and heterogeneous directional propagation patterns that extended beyond those seen previously in humans. Moreover, waves with specific complex shapes correlated with particular cognitive processes. Crucially, we were able to robustly predict a subject’s behavioral state at the single trial level based on the direction and strength of the observed patterns of complex traveling waves which could be the potential basis for a novel brain computer interface. Our findings provide a fundamental new advance in explaining how the brain dynamically reorganizes large-scale neuronal processes that underlie complex human behaviors.