The period of Alexander the Great and the Roman empire were the time that siege engines became more and more professional.
Demetrius 'poliorcetes' (the besieger) built the largest siege tower known in history. It was 40-43 meters high, needed 200 men to get it going, had 8 floors and contained 16 bolt throwers. After he managed to take the walls of Rhodes and break them down, he discovered that the enemy had built a new wall behind the wall he just managed to take...
He never took the city, and afterwards the people of Rhodos built the Colossus of Rhodes (one of the seven wonders of the world in ancient times, next to the pyramids, etc.) from the towers he left behind.
Bolt Throwers and Stone Throwers
The models above are both from Hinchliffe. The models below are wooden models 1:12 from Mantua.
All these machines were used not only on the battlefield, but also to use in sieges. Click <here> to read a battle report of a Siege we played with the Siege supplement.
A Marching Camp
When travelling in hostile territory you had to defend your camp. The Romans were experts in building marching camps. Their soldiers were able to build a new camp every day, with a wall, , wooden stakes the soldiers took with them on their march, a ditch and watchtowers.
The Seleucids and Pontic army kept using chariots, an old custom in the east. But not as missile platforms. No, these chariots were designed to smash into the enemy lines. For that reason they had scythes attached to the chariot.