To support a range of behaviors, the brain must flexibly coordinate neural activity across widespread brain regions. One potential mechanism for this coordination is a traveling wave, in which a neural oscillation propagates across the brain while organizing the order and timing of activity across regions (Ermentrout & Kleinfeld, 2001; Muller et al., 2018). Although traveling waves are present across the brain in various species (Lubenov & Siapas, 2009; Zhang et al., 2018; Davis et al., 2020), their potential functional relevance remained unknown. Here, using rare direct human brain recordings, we demonstrate two novel functional roles for traveling waves of theta- and alpha-band (2-13 Hz) oscillations in the cortex. First, traveling waves propagate in different directions during separate cognitive processes. In episodic memory, traveling waves tended to propagate in posterior-to-anterior and anterior-to-posterior directions, respectively, during encoding and retrieval. Second, traveling waves are informative about the timing of behavior, with the phase of ongoing traveling waves indicating when subjects would retrieve memories. Because traveling waves of oscillations correspond to local neuronal spiking, these patterns indicate that rhythmic pulses of activity move across the brain with different directions and timing for separate behaviors. More broadly, our results suggest a fundamental role for traveling waves and oscillations in dynamically coordinating neural connectivity, by flexibly organizing the timing and directionality of network interactions across the cortex to support cognition and behavior.