Giant star clusters were an important evolutionary element of the early universe, and they appear to be qualitatively different from smaller star clusters such as those currently forming in the Milky Way. Theory suggests that massive stars are crucial to their formation and long-term survival. Stellar winds, paradoxically, may be the key to the inhibition of gas dispersal and feedback that allows the growth of the cluster. I discuss how observations of extragalactic super star clusters with the VLA and ALMA are helping us understand how these clusters form and grow.