The interest in cyclopropane derivatives is caused by the facts that, first, the three-carbon ring is present in quite a few natural and biologically active compounds and, second, compounds with this ring are convenient building blocks for the synthesis of diverse molecules (acyclic, alicyclic and heterocyclic). The carbon–carbon bonds in cyclopropane are kinetically rather inert; hence, they need to be activated to be involved in reactions. An efficient way of activation is to introduce vicinal electron-donating and electron-withdrawing substituents into the ring; these substrates are usually referred to as donor-acceptor cyclopropanes. This review gives a systematic account of the key methods for the synthesis of donor-acceptor cyclopropanes. The most important among them are reactions of nucleophilic alkenes with diazo compounds and iodonium ylides and approaches based on reactions of electrophilic alkenes with sulfur ylides (the Corey – Chaykovsky reaction). Among other methods used for this purpose, noteworthy are cycloalkylation of CH-acids, addition of α-halocarbonyl compounds to alkenes, cyclization via 1,3-elimination, reactions of alkenes with halocarbenes followed by reduction, the Simmons – Smith reaction and some other. The scope of applicability and prospects of various methods for the synthesis of donor-acceptor cyclopropanes are discussed. The bibliography includes 530 references.