This document summarizes hydrogen production through solid oxide electrolysis. It discusses how solid oxide electrolysis cells (SOECs) can efficiently produce hydrogen or syngas from electricity and unused heat. SOECs operate at high temperatures and can take advantage of excess renewable energy through water electrolysis, storing the energy as hydrogen. The document outlines the key materials used in SOECs, including yttria-stabilized zirconia as the electrolyte and lanthanum strontium manganite and nickel cermet as the oxygen and hydrogen electrodes. Co-electrolysis of steam and carbon dioxide via SOECs is also presented as a method to produce syngas for liquid fuels while recycling carbon dioxide.