As one of the abundant and inexpensive metals on the earth, copper has demonstrated broad applications in synthetic chemistry and catalysis. Among these copper-catalyzed advances, copper carbenes are versatile and reactive intermediates that can mediate a variety of transformations, which have attracted much attention in the past decades. The present review summarizes two different reaction models that take place between a copper carbene intermediate and alkyne species, including the cross-coupling reaction of copper carbene intermediate with terminal alkyne, and the addition of copper carbene intermediate onto the C–C triple bond. This article will cover the profile from 2010 to 2021 by placing emphasis on the detailed catalytic models and highlighting the synthetic applications offered by these practical and mild methods.