Recent advances in attention research have been propelled by the debate on target enhancement versus distractor suppression. A predominant neural signature of attention is the modulation of alpha oscillatory power (~10 Hz), which signifies shifts of attention in time, space, and between sensory modalities. However, the underspecified functional role of alpha oscillations limits the progress of tracking down the neuro-cognitive basis of attention. Here, we review and critically examine a synthesis of three conceptual and methodological aspects that are indispensable for alpha oscillations as a neural signature of attention. First, precise anatomical mapping of neural signals reveals distinct alpha oscillators that implement facilitatory versus suppressive components of attention. Second, a testable framework enables unanimous association of alpha modulation with either target enhancement or different forms of distractor suppression (active versus automatic). Third, links of anatomically and functionally specified alpha oscillators to behavior reveal the causal nature of alpha oscillators for attention.