An alternative currency (or private currency) is any currency used as an alternative to the dominant national or multinational currency systems. They are created by an individual, corporation, or organization, they can be created by national, state, or local governments, or they can arise naturally as people begin to use a certain commodity as a currency. Mutual credit is a form of alternative currency, and thus any form of lending that does not go through the banking system can be considered a form of alternative currency.
When used in combination with or when designed to work in combination with national or multinational fiat currencies they can be referred to as complementary currency. Most complementary currencies are also local currencies and are limited to a certain region.
Barters are another type of alternative currency. These are actually exchange systems, which only trade items; thus without the use of any currency whatsoever. Finally, LETS is a special form of barter which trades points for items. One point stands for one worker-hour of work.
Often there are issues related to paying tax. Some alternative currencies are considered tax-exempt, but most of them are fully taxed as if they were national currency, with the caveat that the tax must be paid in the national currency. The legality and tax-status of alternative currencies varies widely from country to country; some systems in use in some countries would be illegal in others.