There has been rapid progress and growing interest in alkyne metathesis within the past decade. The availability of highly active catalysts as well as their applications in both organic synthesis and polymer chemistry has served to motivate the advancement of this field. In this article, the development of several different metathesis catalysts, including two heterogeneous ones, are reviewed with an emphasis on comparing strengths and weaknesses. In Section 4, the applications of alkyne metathesis to synthesis of natural products, conjugated polymers as well as shape-persistent macrocycles are discussed. In the last section, a comparison of alkyne metathesis to the well established alkene metathesis is given. Developing an alkyne metathesis catalyst with both high reactivity and robustness to air and moisture remains an unsolved problem of this important and useful reaction.