Warmatrix

The name "condottieri" is Italian and originally meant 'contractors' or 'mercenaries', though the term is used internationally. The condottieri were captains who led mercenary companies. The name is sometimes used for the companies themselves too, though the proper name for them is "condotti".
In Europe, around 1300 CE, there was a transition from the 'feudal' system to a 'mercenary' one. In the former, the nobility provided military services in return for loot, land and privileges. In the latter soldiers were paid in money and written contracts between soldiers and employers were drawn up. Not only the nobility fought for money, but also commoners. Soon, professional mercenaries, drawn from all layers of society, appeared.
The rise of the condottieri started in Italy. In the Late Middle Age the European economy steadily grew and Italy was in the vanguard. Political leaders of small city states there had a lot of money to spend on armies. However there were not many people to recruit from, as most of them were skillful in crafts, trade and arts but untrained in war and often uninterested in a military career. So the kings, dukes, doges and others hired mercenaries from abroad, mostly from Brabant, Germany, Catalonia and Aragon. There were so many wars to fight that several groups of mercenaries did not disband after a war, but stayed together and sought re-employment elsewhere.
The first well organized company was the Ventura company, founded by duke Werner von Urslingen. Another (in)famous one was the Great Catalan Company, led by the Italian noble Ruggiero da Fiore, which fought both for and against the Byzantine empire, in Sicily and in Greece, under da Fiore and other condottieri. At its height it numbered nearly 3,000 men, though most companies were no larger than a few hundred. Others followed, like the White Company of John Hawkwood. In Italy, the mercenary companies gradually consisted less of foreigners, more of native Italians. The most successful condottiere of all was Francesco Sforza, who managed to make himself duke of Milan.
The core of mercenary companies consisted of men-at-arms. They were organized in units called "barbute", 'bearded' helmets, later replaced by "lancia", 'lances'. Each lance consisted of a knight and a sergeant, supplemented by a page and sometimes one or two other non-combatants. Five lances formed a "posta", 'position' and five positions a "bandiera", 'banner'. Banners were rotated into and out of battles to rest fatigued warriors.
Unlike their predecessors, the condottieri fought for wealth instead of honor (though honor implied loot also). They treated each other much better than civilians and even their employers, from whom they stood apart. Condottieri honored their contracts, as a good business reputation was vital to gain new employment after a finished job. Yet they fought for money only and after a contract easily switched sides if another party offered more.
Around 1400 CE they became the dominant military power in Italy. This allowed them to not only serve, but also make and break their employers and dictate the conditions of their employment to their advantage. More and more they evaded harsh winter campaigns and butchering each other in bloody combat. In extreme cases they waged mock-battles that lasted for hours and were full of expressive maneuvers, but saw not a single casualty. However, in other cases they fought fiercely. Generally it was in their interest to score no decisive victories, but keep wars dragging on. If the wars ended, they often turned on their former employers to loot and extort money from them.
Meanwhile European states took the next step in military organization. The Italian city states started to establish companies of "Lance Spezzate", broken lances, mercenaries who were hired individually rather than through condottieri. In 1445 CE Charles VII of France did not disband his army after his latest campaign against the English, but kept it intact, paying their wages with taxes and thus re-establishing a (small) standing army. These state-sponsored armies soon proved themselves superior to the mercenary bands led by condottieri, who tended to stick to obsolete Medieval weapons and tactics. Within a century, condottieri had almost complete vanished from the scene. Yet the phenomenon of mercenaries never entirely disappeared. It still is alive today, in the Swiss Guards who are in employ of the Vatican.