ConspectusCycloaddition reactions are an effective method to quickly build molecular complexity. As predicted by the Woodward-Hoffmann rules, concerted cycloadditions with alkenes allow for the constructions of all possible stereoisomers of product by use of either the Z or E geometry. While this feature of cycloadditions is widely used in, for example, [4 + 2] cycloadditions, translation to [2 + 2] cycloadditions is challenging because of the often stepwise and therefore stereoconvergent nature of these processes. Over the past decade, our lab has explored Lewis acid-promoted [2 + 2] cycloadditions of electron-deficient allenes or ketenes with alkenes. The concerted, asynchronous cycloadditions allow for the synthesis of various cyclobutanes with control of stereochemistry.Our lab developed the first examples of Lewis acid-promoted ketene-alkene [2 + 2] cycloadditions. Compared with traditional thermal conditions, Lewis acid-promoted conditions have several advantages, such as increased reactivity, increased yield, improved diastereoselectivity, and, for certain cases, inverse diastereoselectivity. Detailed mechanistic studies revealed that the diastereoselectivity was controlled by the size of the substituent and the barrier of a deconjugation event. However, these reactions required the use of stoichiometric amounts of EtAlCl2 because of the product inhibition, which led us to investigate catalytic enantioselective [2 + 2] cycloadditions of allenoates with alkenes. Through the use of chiral oxazaborolidines, a broad range of cyclobutanes can be prepared with the control of enantioselectivity. Mechanistic experiments, including 2D-labled alkenes and Hammett analysis, illuminate likely transition state models for the cycloadditions. Additional studies led to the development of Lewis acid-catalyzed intramolecular stereoselective [2 + 2] cycloadditions of chiral allenic ketones/esters with alkenes.The methods we developed have been instrumental in the synthesis of several families of natural products. Specifically, one key lactone motif in (±)-gracilioether F was constructed by a ketene-alkene [2 + 2] cycloaddition and subsequent regioselective Baeyer-Villiger oxidation sequence. Enantioselective allenoate-alkene [2 + 2] cycloadditions allowed for the synthesis of (-)-hebelophyllene E. Another attempt of applying this method in the synthesis of (+)-[5]-ladderanoic acid failed to deliver the desired cyclobutane because of an unexpected rearrangement. The key cyclobutane was later assembled by a stepwise carboboration/Zweifel olefination process. Finally, the stereoselective [2 + 2] cycloadditions of allenic ketones and alkenes was applied in the syntheses of (-)-[3]-ladderanol, (+)-hippolide J, and (-)-cajanusine.