Suicide is a global phenomenon that impacts individuals, families, and communities from all income groups and all regions worldwide. While it can be prevented if personalized interventions are implemented, more objective and reliable diagnostic methods are needed to complement interview-based risk assessments. In this context, electroencephalography (EEG) might play a key role. We systematically reviewed EEG resting state studies of adults with suicide ideation (SI) or with a history of suicide attempts (SAs). After searching for relevant studies using the PubMed and Web of Science databases, we applied the PRISMA method to exclude duplicates and studies that did not match our inclusion criteria. The selection process yielded seven studies, which suggest that imbalances in frontal and left temporal brain regions might reflect abnormal activation and correlate with psychological distress. Furthermore, asymmetrical activation in frontal and posterior cortical regions was detected in high-risk depressed persons, although the pattern in the frontal region was inverted in non-depressed persons. The literature reviewed suggests that SI and SA may be driven by separate neural circuits and that high-risk persons can be found within non-depressed populations. More research is needed to develop intelligent algorithms for the automated detection of high-risk EEG anomalies in the general population.