The tagma (Greek: τάγμα; pl.: tagmata, τάγματα) is a military unit of battalion or regiment size, especially the elite regiments formed by Byzantine emperor Constantine V and comprising the central army of the Byzantine Empire in the 8th–11th centuries.

In its original sense, the term "tagma" (from the Greek τάσσειν tássein, "to set in order") is attested from the 4th century and was used to refer to an infantry battalion of 200–400 men (also termed bandum or numerus in Latin, arithmos in Greek) in the contemporary Eastern Roman army. In this sense, the term continues in use in the current Hellenic Armed Forces (cf. Greek military ranks).

In later usage, the term came to refer exclusively to the professional, standing troops, garrisoned in and around the capital of Constantinople. Most of them traced their origins to the Imperial guard units of the late antique Roman Empire. By the 7th century, these had declined to little more than parade troops, meaning that the emperors were hard put to face the frequent revolts of the new and powerful thematic formations, especially the Opsikion, the Asian theme closest to the capital. Within the first sixty years since its creation, it was involved in five revolts, culminating in the briefly successful rebellion and usurpation of the throne by its komēs (commander), Artabasdos, in 741–743.

After putting down the revolt, Emperor Constantine V (r. 741–775) reformed the old guard units of Constantinople into the new tagmata regiments, which were meant to provide the emperor with a core of professional and loyal troops, both as a defense against provincial revolts, and also, at the time, as a formation devoted to Constantine's iconoclastic policies. The tagmata were exclusively heavy cavalry units, more mobile than the theme troops, and maintained on a permanent basis. During the defensive phase of the Empire in the 8th and 9th centuries, their role was that of a central reserve, garrisoned in and around the capital, in regions such as Thrace and Bithynia. They formed the core of the imperial army on campaign, augmented by the provincial levies of thematic troops, who were more concerned with local defense.

In addition, like in Roman armies of late antiquity, they served as a recruiting and promotion ground for young officers. A career in a tagma could lead to a major command in the provincial thematic armies or a high court appointment, as promising young men had the opportunity to catch the Emperor's attention. Officers in the tagmata came primarily either from the relatively well-off urban aristocracy and officialdom, or the landed aristocracy of the Anatolian themes, which increasingly came to control the higher military offices of the state. Nevertheless, the tagmata, as indeed military and state service in general, offered a degree of upwards social mobility for the lower strata of society.

In their heyday in the 9th and early 10th centuries, there were four tagmata proper ("τὰ δʹ τάγματα"):

Other units closely related to the tagmata, and often included among them, were:

In addition, there was also the Hetaireia (Gr. Ἑταιρεία, "Companions"), which comprised the mercenary corps in Imperial service, subdivided in Greater, Middle and Lesser, each commanded by a respective Hetaireiarchēs.