Capacitive desalination (CD) is a promising desalination technique as, relative to reverse osmosis (RO), it requires no membrane components, can operate at low (sub-osmotic) pressures, and can potentially utilize less energy for brackish water desalination. In a typical CD cell, the feed water flows through the separator layer between two electrically charged, nanoporous carbon electrodes. This architecture results in significant performance limitations, including an inability to easily (in a single charge) desalinate moderate brackish water feeds and slow, diffusion-limited desalination. We here describe an alternative architecture, where the feed flows directly through electrodes along the primary electric field direction, which we term flow-through electrode (FTE) capacitive desalination. Using macroscopic porous electrode theory, we show that FTE CD enables significant reductions in desalination time and can desalinate higher salinity feeds per charge. We then demonstrate these benefits using a custom-built FTE CD cell containing novel hierarchical carbon aerogel monoliths as an electrode material. The pore structure of our electrodes includes both micron-scale and sub-10 nm pores, allowing our electrodes to exhibit both low flow resistance and very high specific capacitance (>100 F g⁻¹). Our cell demonstrates feed concentration reductions of up to 70 mM NaCl per charge and a mean sorption rate of nearly 1 mg NaCl per g aerogel per min, 4 to 10 times higher than that demonstrated by the typical CD cell architecture. We also show that, as predicted by our model, our cell desalinates the feed at the cell's RC timescale rather than the significantly longer diffusive timescale characteristic of typical CD cells.