Dengue virus (DENV) is one of the most significant human viral pathogens transmitted by mosquitoes and can cause from an asymptomatic disease to mild undifferentiated fever, classical dengue, and severe dengue. Neutralizing memory antibody (Ab) responses are one of the most important mechanisms that counteract reinfections and are therefore the main aim of vaccination. However, it has also been proposed that in dengue, some of these class-switched (IgG) memory Abs might worsen the disease. Although these memory Abs derive from B cells by T-cell-dependent processes, we know rather little about the (acute, chronic, or memory) B cell responses and the complex cellular mechanisms generating these Abs during DENV infections. This review aims to provide an updated and comprehensive perspective of the B cell responses during DENV infection, starting since the very early events such as the cutaneous DENV entrance and the arrival into draining lymph nodes, to the putative B cell activation, proliferation, and germinal centers (GCs) formation (the source of affinity-matured class-switched memory Abs), till the outcome of GC reactions such as the generation of plasmablasts, Ab-secreting plasma cells, and memory B cells. We discuss topics very poorly explored such as the possibility of B cell infection by DENV or even activation-induced B cell death. The current information about the nature of the Ab responses to DENV is also illustrated.