IntroductionOrganic synthesis has played a major role in the advancement of modern science and technology by enabling the preparation of natural and designed targets of chemical, biological, medicinal, environmental, and materials importance [1]. This progress and its continuation toward products of even greater value are unique consequences of the design or discovery and development of fundamentally new reactions. New reactions give rise to new synthetic strategies, which in turn allow for more step-economical, if not ideal, approaches to molecules of interest [2]. The synthesis of silphinene (Scheme 13.1) illustrates how a target, requiring typically ten to twenty steps, can be prepared in only three steps based on a new strategy inspired by a new reaction, the arenealkene cycloaddition [3]. New reactions also enable more rapid and efficient access to known and, more importantly, structurally novel chemical libraries. New reactions can also provide benefits in safety, cost, time, resource utilization, and environmental impact, while simultaneously introducing new mechanisms and opportunities for achieving synthetic selectivity (chemo-, regio-, stereo-, and enantioselectivity).Among the classes of new reactions, cycloadditions are of unique value for increasing molecular complexity and thereby achieving step brevity [4]. They allow for the assembly of complex ring systems in a convergent and often selective fashion, generally from simple, readily available building blocks. The Diels-Alder cycloaddition (Scheme 13.2) [5] is illustrative of the enormous utility of such reactions in synthesis, providing a cycloadduct with up to four stereogenic centers in one step. This process has figured prominently in the synthesis of six-membered ring systems found in a wide array of molecules of theoretical, medicinal, and materials value. hm Scheme 13.1 New reactions and step economy: a three-step total synthesis of silphinene.13 Rhodium(I)-Catalyzed [5+2], [6+2], and [5+2+1] Cycloadditions 264 Scheme 13.2 The Diels-Alder reaction: convergency and complexity increase to favor step economy. Scheme 13.3 Representative natural products incorporating medium-sized rings. p p 13.2 Cycloaddition Approaches to Seven-Membered Rings 265 Scheme 13.4 Metal catalysis enables forbidden or difficult noncatalyzed reactions: [4+4] and [4+2] reactions of dienes. 13.3 Design of a Transition Metal-Catalyzed [5+2] Cycloaddition of Vinylcyclopropanes and p-Systems 267 Scheme 13.7 The [5+2] cycloaddition: a conceptual homolog of the Diels-Alder reaction. p p p r p 13 Rhodium(I)-Catalyzed [5+2], [6+2], and [5+2+1] Cycloadditions 268 Scheme 13.8 Metal-catalyzed VCP isomerization and the design of a new reaction. Scheme 13.9 Strain-driven cleavage of metal carbinyl cyclopropanes. 13.6 Cycloaddition Approaches for Eight-Membered Ring Synthesis 291 Scheme 13.17 The first examples of hetero-[5+2] cycloadditions. 13 Rhodium(I)-Catalyzed [5+2], [6+2], and [5+2+1] Cycloadditions 292 Scheme 13.18 Representative examples of transition metal-mediated cycloaddi...