Give a noiseless computer the same input and the same set of instructions and you should get back the same answer every time. Give a human the same sensory input and the same set of instructions and you can get an often-surprising amount of variability in their responses. This observation highlights the fact that perceptual decisions are determined not only by incoming signals from the sensory periphery, but also by the ever-changing internal state of the brain at the moment the input is given. What features of spontaneous brain activity account for such trial-to-trial variability in visual perception? Are these activities stochastic, or can they be sculpted by cognitive states, such as attention or expectations, in order to shape perceptual processing in accordance with one's goals? I'll present experiments that reveal how spontaneous brain activity in the form of ongoing oscillatory dynamics in the 8-13 Hz range (the so-called alpha rhythm) relate to perceptual variability. Different aspects of this oscillatory signal -- the amplitude, phase, and peak frequency -- are found to relate to different aspects of visual perception and can explain a significant amount of trial-to-trial variability in perceptual judgments. The same oscillatory parameters that, when varying spontaneously, predict perceptual variability, are also found to be under the influence of top-down control. Spatial attention, temporal expectations, and task-demands can modulate specific parameters of alpha-band activity in anticipation of an imperative visual stimulus. These experiments isolate specific features of oscillatory brain activity that account for perceptual variability in the face of constant input and bridges a gap between spontaneous brain activity and top-down mechanisms, whereby the latter can capitalize on the former to implement goal-directed control over perceptual processing.