Electrochemical energy storage (EES) devices with high‐power density such as capacitors, supercapacitors, and hybrid ion capacitors arouse intensive research passion. Recently, there are many review articles reporting the materials and structural design of the electrode and electrolyte for supercapacitors and hybrid capacitors (HCs), though these reviews always focus on individual supercapacitors or single HCs. Herein, the conventional capacitor, supercapacitor, and hybrid ion capacitor are incorporated, as the detailed description of conventional capacitors is very fundamental and necessary for the better understanding and development of supercapacitors and hybrid ion capacitors, which are often ignored. Therefore, herein, the fundamentals and recent advances of conventional capacitors, supercapacitors, and emerging hybrid ion capacitors are comprehensively and systematically summarized in terms of history, mechanisms, electrode materials, existing challenges, and perspectives. At the same time, it is believed that a comprehensive and fundamental understanding for capacitor‐related EES devices is provided in the review and has a great guiding role for future development.