This article outlines the fundamental concept to molybdenum imido, tungsten imido and tungsten oxo alkylidene N-heterocyclic carbene (NHC) catalysts for olefin metathesis. Starting from Mo(NR)(CHCMe R')(OTf) ⋅DME (R=alkyl, aryl; R'=CH , Ph; OTf=CF SO ; DME=1,2-dimethoxyethane), W(NR)(CHCMe Ph)X (X=pyrrolide, OR'', SiPh ) and W(O)Cl (CHCMe Ph)(PMe Ph) , respectively, the neutral, pentacoordinated 16-valence electron (VE) complexes became accessible. These serve as precursors for the corresponding cationic, tetracoordinated 14-VE catalysts. This class of olefin metathesis catalysts based on group 6 metal alkylidene NHCs is characterized by a broad structural variability, high activity, high productivity and, in tailored systems, high functional group tolerance even vs. protic groups including alcohols and carboxylic acids. Also, high regio- and stereoselectivity is achieved, both in ring-opening metathesis polymerization (ROMP) and in the cyclopolymerization of α,ω-diynes. Fundamentals concerning the influence of the imido/oxo ligand, the different NHCs and the anionic ligands on catalyst performance and stability as well as reaction pathways are summarized. Also, the concepts for catalyst immobilization, whether via the NHC or by substitution of an alkoxide, are presented. Finally, special features such as the use of betaine-type anionic ligands (alkoxides and sulfonates), which offer access to ionic catalysts for use biphasic reaction setups, are briefly outlined.