In this paper, a brief, preliminary attempt is made to frame a scientific debate about how functional responses at gamma frequencies in electrophysiological recordings (EEG, MEG, ECoG, and LFP) should be classified and interpreted. In general, are all gamma responses the same, or should they be divided into different classes according to criteria such as their spectral characteristics (frequency range and/or shape), their spatial-temporal patterns of occurrence, and/or their responsiveness under different task conditions? In particular, are the responses observed in intracranial EEG at a broad range of "high gamma" frequencies (~60-200Hz) different from gamma responses observed at lower frequencies (~30-80Hz), typically in narrower bands? And if they are different, how should they be interpreted? Does the broad spectral shape of high gamma responses arise from the summation of many different narrow-band oscillations, or does it reflect something completely different? If we are not sure, should we refer to high gamma activity as oscillations? A variety of theories have posited a mechanistic role for gamma activity in cortical function, often assuming narrow-band oscillations. These theories continue to influence the design of experiments and the interpretation of their results. Do these theories apply to all electrophysiological responses at gamma frequencies? Although no definitive answers to these questions are immediately anticipated, this paper will attempt to review the rationale for why they are worth asking and to point to some of the possible answers that have been proposed.