Two complementary catalytic systems are reported for the 1,3-dipolar cycloaddition of azides and iodoalkynes. These are based on two commercially available/readily available copper complexes, [CuCl(IPr)] or [CuI(PPh3)3], which are active at low metal loadings (PPh3 system) or in the absence of any other additive (IPr system). These systems were used for the first reported mechanistic studies on this particular reaction. An experimental/computational-DFT approach allowed to establish that 1) some iodoalkynes might be prone to dehalogenation under copper catalysis conditions and, more importantly, 2) that two distinct mechanistic pathways are likely to be competitive with these catalysts: either through a copper(III) metallacycle or via direct p-activation of the starting iodoalkyne.