A republic is a state or country that is not led by a hereditary monarch,Niccolò Machiavelli, 1532, The Prince, Chapter 1. but in which the people (or at least a part of its people) have impact on its government. The word originates from the Latin term res publica, which literally translates as "public thing" or "public matter".

The organization of republics can vary widely. The first section of this article gives an overview of the characteristics that distinguish different types of republics. The second section of the article gives some short profiles of the most influential republics by way of illustration. A more comprehensive list of republics appears in a separate article. The third section is about how republics are approached as state organizations in political science: in political theory and people governed.

Head of state

In most modern republics the head of state is termed president. Other titles that have been used are consul, doge, archon and many others. In republics that are also democracies the head of state is selected as the result of an election. This election can be indirect, such as if a council of some sort is elected by the people, and this council then elects the head of state. In these kinds of republics the usual term for a president is in the range of four to six years. In some countries the constitution limits the number of terms the same person can be elected as president. This type of democracy was used in Ancient Rome.

If the head of state of a republic is at the same time the head of government, this is called a presidential system (example: United States). In semi-presidential systems and parliamentary republics, where the head of state is not the same person as the head of government, the latter is usually termed prime minister, premier or chancellor. Depending on what the president's specific duties are (for example, advisory role in the formation of a government after an election), and varying by convention, the president's role may range from the ceremonial and apolitical to influential and highly political. The Prime Minister is responsible for managing the policies and the central government. The rules for appointing the president and the leader of the government, in some republics permit the appointment of a president and a prime minister who have opposing political convictions: in France, when the members of the ruling cabinet and the president come from opposing political factions, this situation is called cohabitation. In countries such as Germany and India, however, the president needs to be strictly non-partisan.

In some countries, like Switzerland and San Marino, the head of state is not a single person but a committee (council) of several persons holding that office. The Roman Republic had two consuls, appointed for a year by the senate. During the year of their consulship each consul would in turn be head of state for a month at a time, thus alternating the office of consul maior (the consul in power) and of consul suffectus (the subordinate consul who retained some independence, and held certain veto powers over the consul maior) for their joint term.