The ancient Romans believed that the empire would last forever, so they built things to last a long, long time.
Roman Buildings: The Romans invented an incredible building material concrete. They used it to build the dome of the Pantheon, which even today is still one of the largest single-span domes in the world. The also used concrete to build the Colosseum, the Circus Maximus, and even an underwater port facility at Caesarea (in Israel).
One of the greatest feats of Roman engineers were the Roman roads. These roads were used to connect all parts of the empire to Rome itself. They built thousands of miles of roads.
People still used these roads until the onset of the automobile which were too big to use them. So modern road builders simply widened them a little, covered them with asphalt, and continued to use them as a road bed.
The Romans had another great idea - milestones. A milestone is a large stone marker placed along the side of the road that gave the distance to the nearest city, when that section road was built and who paid for that section of road.
One of the most impressive feats of Roman engineering were the Aqueducts. For drinking, irrigation, and yes even for the public baths, the Romans needed fresh water. As they grew, the Roman cities became too big to get water from wells or even nearby lakes or streams, so the Romans built a way to get water from large lakes and river to where their cities were. These were the Roman aqueducts.
Generally, the Romans built their aqueducts and laid the pipe to carry water underground just like we do today. But, sometimes to keep the pipe level (with just a small drop to keep the water flowing) they had to build aboveground. When they had to cross a valley they built on arches to carry the pipe. The whole project was massive. The Romans had to mine the lead to make the pipes in Spain, build roads to transport the lead, make the pipes, transport the pipes, build the trench or arches to put the pipe in, and do the surveying to make sure the pipe had just the right amount of drop to keep the water flowing at the right amount. Pretty good for an ancient people.