Lithium and sodium are light and highly electronegative elements which form the basis of anodes for high-energy-density battery systems. Their high chemical reactivity requires the use of ionic conductors based on non-aqueous solvents, polymers, solid electrolytes or fused salts. An associated range of cathode materials enables cells to be fabricated with open-circuit voltages from 1.5 to 4.0 V. Practical non-aqueous batteries have energies extending from 100 m Wh primary button cells used to power electric watches to 20 kWh secondary batteries being developed for vehicle traction. Power output also varies dramatically with application, ranging from a cardiac pacemaker power source operating at 25-100 $\mu $W for up to 10 years, to a military lithium thermal battery delivering all of its energy in a 1 s pulse, with a specific power of 5 kW kg$^{-1}$. This wide range of applications demands diverse electrical characteristics which may include low self-discharge, extensive cyclability, prolonged shelf-life, etc., and which in turn call for many different types of battery design and materials. This paper surveys the battery chemistry, materials and design of lithium-based primary and reserve cells and of lithium and sodium-based rechargeable batteries.