We live in an age where batteries have crossed the threshold of being a convenience to a necessity. Billions are spent each year and it is a never-ending race to come up with one that lasts longer, is 100% rechargeable or ultimately one so small it can barely be seen.
Batteries are simply a contained redox reaction that is spontaneous with the flow of electrons being diverted to whatever device it is attached to. The key to a great battery is finding chemicals that provide the maximum amount of energy while not being toxic or costing more than the battery is worth to the consumer.
Electrochemistry, the conversion of chemical energy into electrical energy, can be broken down into two areas, reactions that are spontaneous and those that are not.
Batteries are an example of a spontaneous electrochemical reaction and are often referred to as electrochemical cells. While it might seem counterintuitive to produce a non-spontaneous “cell”, sometimes the final product is worth it and can be made by simply adding electricity.
A battery or cell has two main locations, the anode where oxidation occurs and the cathode where reduction occurs. In order to harness the electrochemical energy that is produced, they are separated from each other.
Electrodes (metals that allow the transfer of electrons) in each location can be attached to an external device to complete the circuit and allow the flow of electrons. Ideally, the electrodes are made of the same material that is being oxidized or reduced. Figure 8.1 above is a diagram (from the Physical Chemistry book) of such a cell.
The cell will continue to provide electricity until the electrodes become “coated” or the chemicals are depleted.  Choosing both the chemicals and/or electrodes is the key to a successful battery.
In electrochemical terms, the reactivity or potential of a species to become reduced is given a numeric value called a reduction potential and is measured in volts. Tables of reduction potentials under specific conditions are available (see Table 8.1 in the physical chemistry textbook) to compare. These tables are merely the reduction half reactions with their potentials. The oxidation half reaction and potential can be obtained by swapping the equation and changing the sign on the potential.
The species most likely to be reduced is written on the bottom. It will have the largest negative potential because spontaneous redox reactions have negative potentials. It is called the oxidizing agent because it forces any species with a smaller negative potential (anything above it) to be oxidized. Remember oxidation and reduction must always occur together.
The overall electrochemical equation is found by adding the oxidation half equation to the reduction half equation with the same number of electrons. The cell potential or voltage is calculated by adding the voltage values. Numerically, the further apart the two reactants are, the more voltage will be produced.
If an electrochemical reaction is favorable, or spontaneous, it usually goes to completion and not into a state of equilibrium. The Nernst equation allows these standard conditions to be manipulated using other conditions such as temperature and concentration.
As stated earlier, the best battery will have the best combination of electrodes, concentrations, chemicals and size. Many have been created over the course of history and it is a huge commercial area that thrives today, section 8.8 of the physical chemistry textbook explores some of these.
Rechargeable batteries require one thing further, the existence of the reactive species to be a solid on both the anode and cathode electrodes! While that sounds simple, it is not.  However, in a market that will pay for the research necessary to find the best possible combinations, better and smaller batteries are on the horizon.