Recombinant vectors based on adeno-associated virus (AAV) have been shown to stably express many genes in vivo without mounting immune responses to vectors or transgenes. Thus, AAV vectors have rapidly become the reagents of choice for therapeutic gene transfer. Yet one of the first translations of AAV gene therapy into humans unexpectedly resulted in only short-term expression of the therapeutic gene accompanied by transient but significant toxicity. Immune responses to the vector capsid were held accountable for these results, confirming that a detailed understanding of the interaction of AAV vectors with the immune system is of great importance for the safety and success of gene therapy applications. Most humans display naturally acquired immunity to AAV; circumventing neutralizing antibodies and memory T-cell responses is challenging, but not impossible. This review will evaluate the strategies that have been proposed to overcome such responses and summarize recent findings about the mechanisms and circumstances that lead to the activation of innate and adaptive immune responses to AAV vector components.