This chapter gives a summary of the recent research efforts devoted to the development of transition metal-catalyzed azide–alkyne click polymerizations (AACPs) and their applications in the preparation of linear and hyperbranched polytriazoles (PTAs) with advanced functions. Cu(i)- and Ru(ii)-catalyzed AACPs can yield 1,4- and 1,5-regioregular PTAs, respectively. Various Cu(i) complexes have been applied as catalysts for AACPs. The produced PTAs showed unique properties, such as luminescence, fluorescence imaging, biodegradability, optical nonlinearity, stimulus-responsiveness, thermal stability, self-assembly and catalytic activity.