HIV-1 vaccine research has obtained an enormous boost since the discovery of many broadly neutralizing antibodies (bnAbs) targeting all accessible sites on the HIV-1 envelope glycoprotein (Env). This in turn facilitated high-resolution structures of the Env glycoprotein in complex with bnAbs. Here we focus on gp41, its highly conserved heptad repeat region 1 (HR1), the fusion peptide (FP) and the membrane-proximal external region (MPER). Notably, the broadest neutralizing antibodies target MPER. Both gp41 HR1 and MPER are only fully accessible once receptor-induced conformational changes have taken place, although some studies suggest access to MPER in the close to native Env conformation. We summarize the data on the structure and function of neutralizing antibodies targeting gp41 HR1, FP and MPER and we review their access to Env and their complex formation with gp41 HR1, MPER peptides and FP within native Env. We further discuss MPER bnAb binding to lipids and the role of somatic mutations in recognizing a bipartite epitope composed of the conserved MPER sequence and membrane components. The problematic of gp41 HR1 access and MPER bnAb auto- and polyreactivity is developed in the light of inducing such antibodies by vaccination.