Alpha oscillations are ubiquitous in the brain, but their role in cortical processing remains a matter of debate. Recently, evidence has begun to accumulate in support of a role for alpha oscillations in attention selection and control. Here we first review evidence that 8-12 Hz oscillations in the brain have a general inhibitory role in cognitive processing, with an emphasis on their role in visual processing. Then, we summarize the evidence in support of our recent proposal that alpha represents a pulsed inhibition of ongoing neural activity. The phase of the ongoing EEG can influence evoked activity and subsequent processing, and we propose that alpha exerts its inhibitory role through alternating microstates of inhibition and excitation. Finally, we discuss evidence that this pulsed inhibition can be entrained to rhythmic stimuli in the environment, such that preferential processing occurs for stimuli at predictable moments. The entrainment of preferential phase may provide a mechanism for temporal attention in the brain. This pulsed inhibitory account of alpha has important implications for many common cognitive phenomena, such as the attentional blink, and seems to indicate that our visual experience may at least some times be coming through in waves.