(1) Antikythera mechanism, a 2000 year old computer.
The Antikythera mechanism is an ancient analog computer designed to calculate astronomical positions.
(2) Hero engine, a rocket style jet engine.
A Hero engine, is a rocket style jet engine which spins when heated. In the 1st century AD, Hero of Alexandria described the device, and many sources give him the credit for its invention.
The aeolipile Hero described is considered to be the first recorded steam engine or reaction steam turbine.
(3) Roman concrete
For an environment as prone to earthquakes as the Italian peninsula, interruptions and internal constructions within walls and domes created discontinuities in the concrete mass. Portions of the building could then shift slightly when there was movement of the earth to accommodate such stresses, enhancing the overall strength of the structure. It was in this sense that bricks and concrete were flexible. It may have been precisely for this reason that, although many buildings sustained serious cracking from a variety of causes, they continue to stand to this day.
For more on Roman concrete, see here:
In a quest to make concrete more durable and sustainable, an international team of geologists and engineers has found inspiration in the ancient Romans, whose massive concrete structures have withstood the elements for more than 2,000 years.
The discovery could help improve the durability of modern concrete, which within 50 years often shows signs of degradation, particularly in ocean environments.
(4) Lycurgus Cup, a Roman glass cage cup made of a dichroic glass.
The particles are only about 70 nanometers across, and embedded in the glass, so they cannot be seen by optical microscopy, and a transmission electron microscope is needed instead.