Generally, this will mean armies rapidly upgrade to swordsmen, completely replacing their role by the Feudal Age. This is hastened by their relative cheapness (stone and wood being utilised for building) during the heavy construction in the new age. They provide double the attack power for the same gold upkeep and food cost
They are fast units and go well supporting Archers and artillery, allowing the ranged units to exchange fire with enemy without melee counterattack (although the enemy ranged units will still return volley fire simultaneously).
They can be improved Infantry Scuta research to improve their ranged-infantry and artillery defenses, vastly improving their ability to counterattack after ranged volleys. This is available for research at the Library once a Classical-2 Blacksmith (Building) is constructed.
There are two specialist variants, but both are very situational upgrades, only more effective on a per unit basis and cheaper training, making them useful in mass raids. Both have double the upkeep cost, but have similar training cost.
When looked at from a long term, upkeep-efficiency basis without upgrades, there are few situations where two swordsmen couldn't do the job just as well: both units are mostly for mercenary/burst massing raids.
The variants are:
Raider variant - faster and extremely cheap to train (mostly food), the Gladius makes an ideal raider.
Guardian variant - slower, armoured variant, Phalanxes. They have more defense per unit, but are costly to maintain.
Barbarians use a variant of swordsman called Cutthroats.
In the Original/First Beta release, players had to research the Blacksmith (and build it) to use Swordsmen. In the current revision of the game, only a Classical Barracks is required to train them. They could be improved with Hardened Swords, and their variants required research to be unlocked.