Rechargeable lithium batteries are basically of two types; lithium metal batteries, and, lithium-ion batteries. Lithium metal batteries (LMB) provide a higher theoretical energy density than the alternatives: their wide commercial availability is limited, however, by the tendency to grow dendrites during cycling. This is a potential hazard and also reduces cycle lifetime. Attempts are being made to suppress dendritic growth either by using solid electrolytes that act as mechanical barriers, or by choosing electrolytes that produce a suitable passivation layer called the solid-electrolyte interphase (SEI). Since there is no entirely successful strategy to inhibit the growth of dendrites, safety concerns have led to the use of the other kind of lithium battery, namely, the lithium-ion battery (LiB).Lithium-ion batteries are now widely employed for a variety of applications in electronic devices, mobile telephones, laptop computers and a large variety of other portable appliances. They possess a very high energy density, are light and compact and show excellent cyclability and reliability. The current commercial Li-ion batteries are based on aprotic organic liquids such as ethylene carbonate or dimethyl carbonate which have high dielectric constant and are thus good solvents for salts; they also show a large window of electrochemical stability. However, their vapor pressure is high, so that they can provoke fires and explosions in case of accidental battery shorts, when low-stability cathodes are used such as oxides. Such safety issues become accentuated in large lithium-ion batteries of interest in electric cars, especially if charge-discharge is carried out at high rates. The safety aspect has thus become a paramount issue in the development of this technology. Another component important for safety issue is the separator. This element must have, among other properties, a good wettability with the electrolyte, so that the choice of the separator is dependent on the choice of the electrolyte, one reason why we have chosen to include them in the same chapter.