The first examples of high-oxidation state ("d 0 ") alkylidene and alkylidyne complexes (of tantalum) were published in 1974 and 1975 [1]. Several years of research were required to show that the principles behind tantalum chemistry could be employed to prepare alkylidene and alkylidyne complexes of Mo, W, and Re in their highest oxidation states (counting the alkylidene as a dianionic ligand and the alkylidyne as a trianionic ligand), and that these high-oxidation state complexes, especially those that contain one or more alkoxide ligands, are efficient catalysts for alkene and alkyne metathesis reactions, respectively. This process has been described in previous reviews [2]. Applications of high-oxidation state catalysts for alkene and alkyne metathesis in organic chemistry have also been reviewed [3], although each of these subjects is reviewed again elsewhere in this series in view of the many recent advancements. This review will focus on isolated and characterized high-oxidation state molybdenum and tungsten alkylidene and metallacyclobutane complexes. Attention will be directed largely toward monoalkoxide pyrrolide (MAP) complexes because they have yielded the majority of new results in the last several years. MAP species have been found to be especially efficient in several Z-selective olefin metathesis reactions, such as homocoupling, cross-coupling, ethenolysis, and ROMP (see Grubbs, Handbook of Metathesis, 2nd Edition, Volume 2, Chapter 7). Most of what is presented here has appeared since a review in 2009 [4].In the last decade, impressive advances have been made in the synthesis of alkylidene and alkylidyne complexes that contain metals from groups 4 [5] and 5 [5i,j,m, 6], especially Ti and V, but -except for the ROMP of norbornene by vanadium complexes -group 4 and 5 metals have not shown wide-ranging activity for olefin metathesis. Well-characterized rhenium(VII) complexes are known to be active for metathesis, and many rhenium(VII) alkylidene and alkylidyne complexes have been isolated [2a], but little attention has been paid to the syntheses of rhenium alkylidene or alkylidyne complexes in the last decade. Theoretical calculations have been carried out on M(X)(CHR ′ )(Y)(Z) complexes