This paper explores the chemical systematics of back-arc basins and the physical processes that give rise to them, making use of published data from the Scotia, Mariana, Lau, and Manus Basins. A new low-pressure fractionation model is used to back-correct data with greater than 5.5 wt.% MgO. Even after hydrous correction, back-arc basin basalts (BABB) have low TiO 2 and FeO contents relative to basalts from other ridges. The low TiO 2 both absolutely and relative to Na 2 O requires a source depletion followed by a Na enrichment. This signature is critical to evaluate the range of mantle temperature at back-arc basins, which is about 100°C. In addition to a subduction component and wedge depletion, BABB reflect a prevalent enriched component akin to enriched ocean ridge basalts worldwide, despite the absence of mantle plumes. Data from the Mariana Basin suggest this component arises from very recent addition of low-degree (low-F) melts, which may be an important general agent of mantle heterogeneity. Important aspects of the back-arc data are the linear relationships among all major element parameters with each other and with water. Previous models involving isothermal, isobaric melting with increasing water contents do not account for these relationships. A constraint on permissible physical models is that both trace element and major element data show no inherited effects from garnet in back-arc basins, which constrains generation and transport of melts from great depth to the base of the melting regime. Quantitative modeling of the effects of water on mantle melting shows that previous conclusions based on the MELTS thermodynamic approach are not consistent with experimental data for the mantle. Our new models can account for the back-arc systematics by mixing between dry, pooled fractional melts, formed similarly to open ocean ridges, with hydrous melts generated from sources enriched in H 2 O, Na 2 O, and K 2 O that have equilibrated at low pressure. Thus, successful physical models must be able to produce melts by these two different mechanisms. The effects of H 2 O in back-arc basin ridges and open ocean ridges contrast markedly. In the open ocean, increased water is associated with lower mean extents of melting, increased TiO 2 contents, and an increased garnet effect. In back-arc basins, increased water is associated with increased extents of melting, lower TiO 2 , and no garnet influence. These differences can be accounted for by contrasts in the melting regimes and tectonic setting of the two environments. In the open ocean, deep, low-degree, hydrous melts are produced in the "wings" of the melting regime and combine with higher degree drier melts produced at a range of shallower pressures. At back-arcs, geometrically and thermally, there is no room for "wings" on the arc side of back-arc spreading centers. On the arc side of the spreading center, where water is added, shallow hydrous melting is important, and melt must get to the surface in the context of descending mantle flow. On the back side, dry melting under relatively anhydrous conditions occurs, similar to open ocean ridges. Mixing between melts from the dry side and the wet side should then lead to the characteristic spectra of parental BABB compositions. Both the geometry of melting and the fact of continual rifting of young lithosphere may contribute to the very different water signatures in the open ocean and back-arc settings.