Identifying biomarkers for major depression is of high importance for improving diagnosis and treatment of this common and debilitating neuropsychiatric disorder, as the field seeks to move toward both personalized and more effective treatments. Here we focus on electroencephalography (EEG) or direct scalp voltage recordings as such a biomarker, with an emphasis on gamma and high gamma oscillations (or "rhythms"). In the last several decades, alpha and theta band rhythms have been found to provide information on depressive state as well as recovery, but the gamma band is less well characterized with respect to depression. We summarize some key findings on gamma rhythms (especially their amplitude) as a biomarker or endophenotype for major depression. These studies suggest: (1) under certain conditions gamma rhythms can distinguish subjects with major depression from healthy controls, (2) gamma may distinguish bipolar disorder from unipolar depression, (3) various pharmacological and non-pharmacological treatments that counteract depression also alter gamma, (4) animal models of depression-like behavior show gamma abnormalities, with changes in gamma associated with therapeutic recovery. The most informative approaches in the future may combine profiles of gamma band power across the brain to assess ratios of activity across regions. Overall we have good evidence to suggest that gamma rhythms may provide objective information on major depressive disease status, but we will need further work to better define the precise measures to follow.