The term porous organic cage (POC) is used to refer to capsular molecular systems that contain only covalent organic bonds within their structural scaffold. Several existing reviews provide an historical overview and comprehensive discussion of these systems. In this review, we have chosen to specifically distinguish between capsules formed under thermodynamic control, that exploit reversible covalent bonds, and those formed under kinetic control (covalent-organic cages; COCs). It is noted, however, that the reversibility of "dynamic" bonds is dependent upon the conditions. A stark example of this are alkynes; generally considered kinetically robust, alkynes can be rendered dynamic under specific metathesis conditions. A prolonged discussion on this will not be provided here, but we simply wish to highlight this blurring of lines between different types of POCs.