The compositions of back-arc basin basalts (BABB) can usefully be viewed as products of four factors: (1) the composition of inflowing mantle and its preconditioning during flow to the site of melting; (2) the influx of a subduction component into the arc-basin system; (3) the nature of the interaction between the mantle and subduction components; (4) the melting of water-rich mantle and the assimilation/ crystallization history of the resulting hydrous magma. Geochemical mapping using Nb/Yb as a mantle flow tracer indicates that mantle flow in arc-basin systems varies according to contributions from subduction-driven corner flow, flow around subduction edges, and deflection by barriers to flow. Geochemical mapping using Ba/Nb as a subduction tracer indicates that the magnitude of the subduction input is a function primarily of basin evolution, mantle flow patterns, and arc proximity. The subduction component may reach the back-arc by mixing with ambient mantle, by direct addition of a subduction component, by addition of a hydrous mantle melt, or by incorporation of a component stored in mantle lithosphere. Trace element and water contents of back-arc glasses indicate that decompression melting beneath back-arc basins is augmented by flux melting but suppressed by mixing with depleted mantle. Cl-K systematics indicate that water in back-arc basin magmas may be augmented by assimilation of hydrated ocean crust. The increased water content of primary BABB magmas leads to enhanced olivine and oxide crystallization, and to fluid exsolution at depth, both of which will influence the composition and architecture of the resulting back-arc oceanic crust.