Metathesis is a reversible process and involves an exchange of bonds between two reacting molecules. Metathesis has matured to be a powerful methodology and a universal tool in hydrocarbon synthesis. This chapter extensively reviews metathesis and summarizes the progress such as metal carbenes as intermediates in ring-closing metathesis, synthesis and developments of metathesis catalysts, and green aspects of the use of ruthenium. In the metathesis reaction, alkenes are converted to mixtures of lower and higher alkenes through the interchange of groups on the double bonds in an equilibrium process. Metathesis of alkynes is a less general reaction and has not received the same attention of alkene metathesis. Recent observations, however, have shown that it has the potential of useful applications emerging as a new synthetic tool. Mechanistic studies revealed that alkyne metathesis and ring-opening metathesis polymerization of cycloalkynes proceed via metal carbyne complexes.