Carbo- and heterocyclic structures containing nitrogen-substituted stereocenters are recurrent structural motifs in natural and bioactive compounds, therefore constituting a privileged class of synthetic targets. In this regard, substituted three- and four-membered carbocycles are powerful building blocks. Activation by a catalyst allows for an efficient exploitation of their ring strain, enabling a large variety of transformations. In particular, activation via oxidative addition by transition metals has been widely applied in annulations of these rings. Another common mode of activation consists in the use of Lewis acids to promote heterolytic ring opening of electron-poor strained rings, among which donor-acceptor cyclopropanes and cyclobutanes stand out for their well-established and broad chemistry. In this thesis, intermolecular annulations of three-membered carbocycles via oxidative addition by transition metals were first investigated. We mainly focused on the use of aminocyclopropanes as well as more strained aminomethylidenecyclopropanes. Despite a broad screening of transition metal complexes and modifications of the cyclopropane structure, no desired product could be formed. The use of aminomethylidene cyclopropanes in Lewis acid catalyzed intermolecular annulations was also studied. Employing aldehydes as reaction partners delivered highly functionalized 2-aminotetrahydrofurans. Instead, the use of all-carbon dipolarophiles for the synthesis of carbocycles was not successful. Subsequently, we explored enantioselective transformations of donor-acceptor cyclopropanes. We first investigated a new Lewis acid catalyzed DYKAT of donor-acceptor aminocyclopropanes with 2-siloxyfurans as dipolarophiles. After a thorough optimization, the desired product could be obtained in high er. However, the yield was not satisfactory, and any attempt to improve it by modifying the structure of the aminocyclopropane or by screening additives and reaction conditions was unsuccessful. On the other hand, we succeeded in the development of the first Lewis Acid catalyzed enantioselective desymmetrization of donor-acceptor meso-diaminocyclopropanes. The methodology consists in a copper(II) catalyzed Friedel-Crafts alkylation of indoles and a pyrrole, and delivers enantioenriched urea derivatives, which are recurrent structures in natural and bioactive compounds. The reaction tolerates electronically and sterically diverse substituents on the benzene ring of the indole. The choice of appropriate protecting groups on the cyclopropane was required to guarantee its solubility and to maintain good levels of enantioselectivity. The modification of an underexplored subclass of bisoxazoline ligands, bearing bulky diarylmethanol groups in alpha to the nitrogen atoms, was essential for obtaining high enantiomeric ratios, and led to the synthesis of several novel ligands. Finally, we developed Lewis acid catalyzed [4+2] annulations of donor-acceptor aminocyclobutanes with aromatic aldehydes, which afforded useful 2-aminotetrahydropyrans. A scandium catalyst was employed for the annulation of unsubstituted aminocyclobutanes, which delivered products in yields up to 95% and diastereoselectivities up to 17:1. On the other hand, one equivalent of a cheap and non-toxic iron Lewis acid was required for substituted aminocyclobutanes, which afforded densely functionalized six-membered heterocycles bearing three stereocenters in diastereoselectivities up to 5:1.