**Study Overview:** Cluster headaches are severe, one-sided headaches that come in patterns. This study checks how different parts of the brain communicate during these headaches using a special test called **HD-EEG** (High Density Electroencephalogram). This test captures the brain's electrical activity to see how well different areas are connected when someone has a headache versus when they don't. **Key Points:** - **Study Duration and Visits:** Episodic cluster headache patients will have two visits; during headache times and when they are free of headaches for two weeks. Chronic headache patients and healthy people will have one visit. - **Part of the Study:** Participants will do four short brain activity recordings, with eyes open and closed, during each visit. - **Eligibility:** To join, you must have had cluster headaches for at least a year and not be on certain medications during the study. Some people, like those with epilepsy or pregnant women, cannot participate to ensure safety. This study helps understand brain changes during headaches, which may lead to better treatments.