The generation of HIV bnAbs may be one of the greatest feats of the human immune system and our best hope of finally creating an HIV vaccine. The striking amount of somatic hypermutation in HIV bnAbs led to the hypothesis that T follicular helper (Tfh) cells and germinal centers (GC) play a critical role in the ability of the immune system to generate these uncommon antibodies. In this review, we first summarize what is known about the immunological process of HIV bnAb development, the challenges of eliciting bnAbs via immunizations, and the putative central roles of Tfh cells and GC in the generation of HIV bnAbs. Next, we explore factors that have impeded our understanding of the GC and Tfh-cell processes involved in bnAb generation, including the difficulty of quantifying antigen-specific GC Tfh cells and the difficulty of tracking GC in human and non-human primate vaccine studies. Finally, we discuss antibody immunodominance pertaining to neutralizing antibody generation and the GC response, propose models to explain the negative effects of immunodominance on neutralizing antibody generation, and consider means of optimizing Tfh and GC responses to potentially overcome these problems.