Preparation of substituted cyclobutanes and cyclobutenes by cyclo-addition reactions of alkene and alkyne has become an important synthetic reaction and where applicable is the method of choice for four-membered carbon ring compounds. Such cycloadditons may be achieved thermally under autogeneous pressure in the presence of free-radical inhibitors or photochemically by irradiation with visible or ultraviolet light. The establishment of cyclobutane structure proved an example of waxing and waning in the interpretation of organic reactions. Many studies were done and they are discussed. A breakthrough came with the discovery by DuPont that octafluorocyclobutane can be formed readily by thermal dimerization of tetrafluoroethylene. Several developments followed. The cycloaddition illustrates two important points. First, fluorinated alkenes may add to non-fluorinated unsaturated compounds much more readily than they dimerize. Second, when fluorinated alkenes are given a choice between four- and six-membered rings, as is possible with a conjugated diene, the formation of the four-membered ring is favored. This chapter gives information on the various studies done on this reaction, The scope, limitations, and comparison of added reactivities are detailed.