The alkyl group is the most common component of organic molecules and the most difficult to selectively functionalize. The development of catalysts for dehydrogenation of alkyl groups to give the corresponding olefins could open almost unlimited avenues to functionalization. Homogeneous systems, or more generally systems based on molecular (including solid-supported) catalysts, probably offer the greatest potential for regio- and chemoselective dehydrogenation of alkyl groups and alkanes. The greatest progress to date in this area has been achieved with pincer-ligated transition-metal-based catalysts; this and related chemistry are the subject of this review. Chemists are still far from achieving the most obvious and perhaps most attractive goal in this area, the dehydrogenation of simple alkanes to yield alkenes (specifically monoenes) with high yield and selectivity. Greater progress has been made with tandem catalysis and related approaches in which the initial dehydrogenated product undergoes a desirable secondary reaction. Also reviewed is the substantial progress that has been made in the closely related area of dehydrogenation of alkyl groups of substrates containing heteroatoms.