What are some of Rome's greatest achievements and when were they?
This is a great question. As you undoubtedly know, the Romans were a great empire for a very long time. Hence, to know dates as well as achievements is important.
The Roman were amazing engineers. For example, they made many aqueducts throughout their history. Here is a sample of when a few of them were made. Aqua Appia was built in 311 B.C.; Aqua Anio Vetus was built in 272 - 269 BC; Aqua Marcia was built in 144 - 140 BC and it was 56 miles long; Aqua Anio Novus was built in AD 52 and the length was 54 miles.
The Romans also created some great structures. One of the most famous of these was the Colosseum. The Flavians built it and it was made from 70 - 80 AD.
Finally, we can say that one of the most enduring achievements of the Romans was their law codes. The history of this is long. It started with the Twelve Tables, which date to 451 B.C. From there the law developed into Justinian's Digest, which was complied during his reign (ruled 527-565 CE).