An electrochemical cell consists of two electrodes, which are simply metallic conductors, in contact with an ionic conductor called the electrolyte. (Though the most commonly encountered electrolytes are ionic solutions, they may also be liquids, e.g. molten potassium bromide, or solids, e.g. solid silver iodide. The only criterion is that the substance must be an ionic conductor.)

A single electrode and its electrolyte makes up an electrode compartment. The two electrodes in a cell may share the same compartment, if they have the same electrolyte. Otherwise the two compartments are joined by a salt bridge, typically a concentrated electrolytic solution in a matrix such as agar jelly.

The purpose of the salt bridge is purely to complete the electrical circuit and allow the cell to function. 

The various kinds of electrode/electrolyte combination are tabulated below, with explanatory notes following:

Electrode type Notation Redox Couple Half-reaction
Metal/metal ion M(s)|M+(aq) M+/M M+(aq) + e  =>  M(s)
Gas electrode (i) Pt(s)|X2(g)|X+(aq) X+/X2 X+(aq) + e => ½X2(g)
Gas electrode (ii) Pt(s)|X2(g)|X(aq) X2/X ½X2(g) + e => X(aq)
Metal/insoluble salt M(s)|MX(s)|X(aq) MX/M,X MX(s) + e => M(s) + X(aq)
Redox Pt(s)|M+(aq),M2+(aq) M2+/M+ M2+(aq) + e => M+(aq)

Note that by convention, half-reactions are written as reduction (electron gain) processes.

However, depending upon the redox potential of the other electrode in the cell, it may actually be the reverse, oxidation process which occurs at the electrode. (The oxidation process occurs at the electrode composed of the more easily oxidised metal, and vice versa.)

The metal/metal ion electrode system is usually the first type people encounter. A typical example would be a metal electrode dipped into an aqueous solution of a salt of that metal. Electron transfer occurs between the metal atoms of the electrode and the metal ions in solution.

The gas electrodes are essentially very alike. They typically consist of a platinum electrode dipped into a solution containing the anion or cation of the gas in question. The gas is bubbled slowly over the surface of the platinum electrode. Electron transfer occurs between the gas and the ions in solution. The platinum is present to catalyse the reaction by providing a surface area for it to take place on, and to act as a source or acceptor of electrons. Platinum (or a similar inert metal) is chosen to avoid the possibility of reaction with the gas or solution.

The metal/insoluble salt electrode normally consists of a metal electrode in contact with (partially coated with a thin layer of) an insoluble salt of the metal. This assembly is then held in contact with a solution containing the anion of the insoluble salt. Electron transfer occurs between the metal atoms of the electrode and the metal ions in the insoluble salt.

The redox electrode consists of a solution containing ions of a metal in two different oxidation states. e.g.  an aqueous solution with one mole of  Fe(NO3)2 and one mole of Fe(NO3)3 dissolved in it would be suitable, as it contains both Fe (II) and Fe (III) ions. An inert metal electrode must be dipped into the solution to act as a source or acceptor of electrons and allow the electrode system to be linked to another electrode to create a complete cell.

There are two basic types of electrochemical cell. A galvanic cell is one which generates electricity as a result of the cell reaction, which is a spontaneous (thermodynamically favourable) process. In an electrolytic cell, a non-spontaneous cell reaction is driven to occur by the application of an external source of current. These two types of cell are in many ways direct opposites – the cell reaction of a galvanic cell can be reversed in an electrolytic cell with a sufficient source of external current.