All three nations have the same four basic professions as well as one additional profession:
Engineer - The most important profession, engineers can build and upgrade structures, as well as repair damage done to them by the enemy. They can also be used to collect and transport crates, siberite and oil. Your men can be issued engineering equipment at the depot and the storehouse. Engineers do not carry any heavy weapons, their only way to defend themselves is using their pistol. They can be invaluable against enemy structures however, due to their ability to de-construct them.
Mechanic - Builds and maintains your vehicles at the workshop or factory. A mechanic has the ability to conduct field repair on damaged vehicles, and can also push a vehicle to a depot should it run out of fuel. Mechanics are also able to steer remote controlled vehicles when ordered into a control tower. Mechanic equipment is issued at the factory and the workshop. Just like engineers, mechanics use only pistols for their personal defence.
Scientist - Researches tasks at the laboratory, but can also act as a field medic. With appropriate research scientists can be used to find oil and siberite deposits, tame apemen, destroy siberite sources and calculate teleport exits. Scientist equipment is issued at the laboratory. The scientist has only a pistol for his own defence.
Soldier - The basic attack unit. A soldier's standard issue equipment is an assault rifle and personal armour. Soldiers are also trained in war tactics, and can use their prone ability to conceal themselves from the enemy in difficult terrain. Equipment can be issued at the barracks or armoury.
Sniper - American special unit. Snipers are strong against enemy infantry, and can even be used to snipe drivers out of vehicles. They also have a longer range of sight. With appropriate research a sniper can also be issued pacifying darts, which will put a designated target to sleep for a short while, making him unable to shoot or escape.
Bazooka soldier - Russian special unit. The bazooka soldier is extremely effective against vehicles and buildings, with a long attack range (though not as long as a sniper's). He wears stronger armour than other infantry units, but moves slower as a result. With appropriate research this soldier can also be issued special rockets that can either slow down time in a given radius or teleport people away from the point of impact.
Mortar operator - Arabian special unit. The mortar soldier is excellent against enemy buildings and infantry, excelling over most units with their range. The mortar round however is slow, and will have problems hitting units that move quickly. The operator's armour is slightly thinner than a bazooka soldier's one, but the mortar operator also moves faster than the bazooka soldier.
Desert warrior - Many of the sheikhs in the Arabian legions continue to use traditional weaponry as their main offensive capability. They sport a bolt rifle in addition to their trademark scimitar. They can also tame sabretooth tigers and mastodons for their entourage, and can even ride a mastodon into battle. Desert warriors are special units that cannot be trained.
Every nation also has the ability to tame and use apemen for their goals, though the way in which they use apemen usually differs...
Apeman - Tamed apeman without any equipment or weaponry. Can only attack by clawing at enemies.
Apeman Engineer - Trained by Russians and Americans in their respective depots and warehouses. Can repair or upgrade buildings, but cannot begin constructing them. Can only attack by clawing at enemies.
Apeman Soldier - An apeman with basic rifle training. Can't do much more than point and shoot, not good for much more than cannon fodder. Trained by Russians and Arabs.
Kamikaze Apeman - Trained by Arabs, this apeman is equipped with an explosive vest and trained to run directly at an enemy target. The explosives can be detonated remotely, killing the apeman and anyone unfortunate enough to be nearby at the time of the explosion. Like any other offensive infantry, can be trained in the barracks or armoury.