This study provides a unifying framework for extratropical low-pressure systems with tropical characteristics like nearly axisymmetric inner cores, eyes, and spiral bands. These characteristics can be found, e.g., in subtropical cyclones, polar lows, and medicanes. The authors propose to call these cyclones CYCLOPs, which refers to "cyclones from locally originating potential intensity". The paper presents several case studies to explain and illustrate the new concept, and therefore the paper is also of particular educational value.