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Heraldic design on a shield, surcoat or tabard

A coat of arms is a heraldic visual design on an escutcheon (i. e., shield), surcoat, or tabard (the latter two being outer garments). The coat of arms on an escutcheon forms the central element of the full heraldic achievement, which in its whole consists of a shield, supporters, a crest, and a motto. A coat of arms is traditionally unique to the armiger (e. g. an individual person, family, state, organization, school or corporation). The term "coat of arms" itself, describing in modern times just the heraldic design, originates from the description of the entire medieval chainmail "surcoat" garment used in combat or preparation for the latter. Rolls of arms are collections of many coats of arms, and since the early Modern Age centuries, they have been a source of information for public showing and tracing the membership of a noble family, and therefore its genealogy across time.

The French system of heraldry greatly influenced the British and Western European systems. Much of the terminology and classifications are taken from it. However, with the fall of the French monarchy (and later Empire) there is not currently a Fons Honorum (power to dispense and control honors) to strictly enforce heraldic law. The French Republics that followed have either merely affirmed pre existing titles and honors or vigorously opposed noble privilege. Coats of arms are considered an intellectual property of a family or municipal body. Assumed arms (arms invented and used by the holder rather than granted by an authority) are considered valid unless they can be proved in court to copy that of an earlier holder.

In the heraldic traditions of England and Scotland, an individual, rather than a family, had a coat of arms. In those traditions coats of arms are legal property transmitted from father to son; wives and daughters could also bear arms modified to indicate their relation to the current holder of the arms. Undifferenced arms are used only by one person at any given time. Other descendants of the original bearer could bear the ancestral arms only with some difference: usually a colour change or the addition of a distinguishing charge. One such charge is the label, which in British usage (outside the Royal Family) is now always the mark of an heir apparent or (in Scotland) an heir presumptive. Because of their importance in identification, particularly in seals on legal documents, the use of arms was strictly regulated; few countries continue in this today. This has been carried out by heralds and the study of coats of arms is therefore called "heraldry". In time, the use of arms spread from military entities to educational institutes, and other establishments.

In the Nordic countries, provinces, regions, cities, and municipalities have coats of arms. These are posted at the borders and on buildings containing official offices, as well as used in official documents and on the uniforms of municipal officers. Arms may also be used on souvenirs or other effects, given that an application has been granted by the municipal council.

At a national level, "coats of arms" were generally retained by European states with constitutional continuity of more than a few centuries, including constitutional monarchies like Denmark as well as old republics like San Marino and Switzerland. In Italy the use of coats of arms was only loosely regulated by the states existing before the unification of 1861. Since the Consulta Araldica, the college of arms of the Kingdom of Italy, was abolished in 1948, personal coats of arms and titles of nobility, though not outlawed, are not recognised. Coats of arms in Spain were generally left up to the owner themselves, but the design was based on military service and the heritage of their grandparents. In France, the coat of arms is based on the Fleur de lys and the Rule of Tinctures used in English heraldry as well.

The monarch of Canada's prerogative to grant armorial bearings has been delegated to the Governor General of Canada. Canada has its own Chief Herald and Herald Chancellor. The Canadian Heraldic Authority, the governmental agency which is responsible for creating arms and promoting Canadian heraldry, is situated at Rideau Hall.

The Great Seal of the United States uses on the obverse as its central motif a heraldic achievement described as being the arms of the nation. The seal, and the armorial bearings, were adopted by the Continental Congress on 20 June 1782, and is a shield divided palewise into thirteen pieces, with a blue chief, which is displayed upon the breast of an American bald eagle. The crest is thirteen stars breaking through a glory and clouds, displayed with no helm, torse, or mantling (unlike most European precedents). Only a few of the American states have adopted a coat of arms, which is usually designed as part of the respective state's seal. Vermont has both a state seal and a state coat of arms that are independent of one another (though both contain a pine tree, a cow and sheaves of grain); the seal is used to authenticate documents, whilst the heraldic device represents the state itself.

The Vatican City State and the Holy See each have their own coat of arms. As the papacy is not hereditary, its occupants display their personal arms combined with those of their office. Some popes came from armigerous (noble) families; others adopted coats of arms during their career in the Church. The latter typically allude to their ideal of life, or to specific pontifical programmes. A well known and widely displayed example in recent times was Pope John Paul II's arms. His selection of a large letter M (for the Virgin Mary) was intended to express the message of his strong Marian devotion. Roman Catholic dioceses are also each assigned a coat of arms, as are basilicas or papal churches, the latter usually displaying these on the building. These may be used in countries which otherwise do not use heraldic devices. In countries like Scotland with a strong statutory heraldic authority, arms will need to be officially granted and recorded.

Flags are used to identify ships (where they are called ensigns), embassies and such, and they use the same colors and designs found in heraldry, but they are not usually considered to be heraldic. A country may have both a national flag and a national coat of arms, and the two may not look alike at all. For example, the flag of Scotland (St Andrew's Cross) has a white saltire on a blue field, but the royal arms of Scotland has a red lion within a double tressure on a gold (or) field.

Among the states ruled by communist regimes, emblems resembling those of the Soviet states were adopted in all the Warsaw Pact states except Czechoslovakia and Poland. Since 1986–1989, some of the ex Communist states, such as Russia, have reused their original pre communist heraldry, often with only the symbols of monarchy removed. Other countries such as Belarus have retained their communist coats of arms or at least kept some of the old heraldry. With the independence of the modern nation states of the Arab World from the First World War onwards, European traditions of heraldry were partially adopted for state emblems. These emblems often involve the star and crescent symbol taken from the Ottoman flag. Other commonly seen symbols are birds, chiefly the Eagle of Saladin, and the Hawk of Quraish. These symbols can be found on the coat of arms of Egypt, and Syria, amongst others. Sub Saharan African flags and emblems after decolonisation often chose emblems based on regional traditions or wildlife. Symbols of a ritual significance according to local custom were generally favoured, such as the leopard in the arms of Benin, Malawi, Somalia, the Democratic Republic of the Congo and, in the form of the black panther, of Gabon. In Kenya, the Swahili word Harambee (lit. "Let us come together") is used as a motto in the country's coat of arms. In Botswana and Lesotho, meanwhile, the word Pula (lit. "Rain") is used in like fashion. In the coat of arms of Eswatini, a lion and an elephant serve as supporters. They are each intended to represent the king and the queen mother respectively, the nation's joint heads of state.

Japanese emblems, called kamon (often abbreviated "mon"), are family badges which often date back to the 7th century, and are used in Japan today. The Japanese tradition is independent of the European, but many abstract and floral elements are used.