Herodotus

Herodotus describes the ‘Immortals’ as being heavy infantry, led by Hydarnes; it provided the professional corps of the Persian armies and was kept constantly at a strength of exactly 10,000 men. He stated that the unit’s name stemmed from the custom that every killed, seriously wounded, or sick member was immediately replaced with a new one, maintaining the corps as a cohesive entity with a constant strength.
The Persian denomination of the unit is uncertain. This elite corps is only called the ‘Immortals’ in sources based on Herodotus. There is evidence of the existence of a permanent corps from Persian sources, which provided a backbone for the tribal levies who made up the bulk of the Achaemenid armies.[citation needed] These do not however record the name of “Immortals”. It is suggested that Herodotus’ informant has confused the word anûšiya- (“companion”) with anauša- (“immortal”), but this theory has been criticized by Rudiger Schmidt.[2]
History
The Immortals played an important role in Cambyses II’s conquest of Egypt in 525 BC and Darius I’s invasion of ancient India’s smaller western frontier kingdoms (western Punjab and Sindh, now in Pakistan) and Scythia in 520 BC and 513 BC. Immortals participated in the Battle of Thermopylae 480 BC and were amongst the Persian occupation troops in Greece in 479 BC under Mardonius.
During the final decades of the Achaemenid empire, the role expected of the hazarapatish (commanding officer) of the Immortals was extended to include that of chief minister to the king. The provision of a bodyguard, in direct attendance on the monarch, had already been allocated to a select thousand strong detachment of the corps.
Equipment

Xenophon (Cyropaedia 6.4.1; 7.1.2) describes the guard of Cyrus the Great as having bronze breastplates and helmets, while their horses wore bronze chamfrons and peitrels together with shoulder pieces which also protected the rider’s thighs. Herodotus, instead, describes their armament as follows: wicker shields covered in leather, short spears, quivers, swords or large daggers, slings, bow and arrow. Underneath their robes they wore scale armour coats. The spear counterbalances of the common soldiery were of silver; to differentiate commanding ranks, the officers’ spear butt-spikes were golden. The regiment was followed by a caravan of covered carriages, camels, and mules that transported their supplies, along with concubines and attendants to serve them; this supply train carried special food that was reserved only for their consumption.
The headdress worn by the Immortals is believed to have been the Persian tiara. Its actual form is uncertain, but some sources describe it as a cloth or felt cap which could be pulled over the face to keep out wind and dust in the arid Persian plains. Surviving Achaemenid colored glazed bricks and carved reliefs represent the Immortals as wearing elaborate robes, hoop earrings and gold jewelry, though these garments and accessories were most likely worn only for ceremonial occasions.