Roman concrete was called opus caementicium. The Romans had two main sources of the right kind of volcanic ash in Italy, the main one in Pozzuoli (http://en.wikipedia.org/wiki/Pozzolan) but apparently they mined other places, such as in Eifel where it is known as Trass (http://en.wikipedia.org/wiki/Trass). For example concrete was used in the very extensive aquaducts serving the Roman city that is now Cologne.
It is very similar to lime plaster (lime and sand) and so it is thought to have been discovered by simple substitution of local pozzolan for sand.
The advantage of Portland cement is that it cures very quickly. Roman cement takes something like a month to cure.
Another apparent advantage of Roman concrete is that they were able to throw up large structures with concrete vaults or domes with a large workforce in relatively short time frames, whereas the Medieval cathedrals (which were based initially on the same Roman basilica) took a smaller, highly skilled workforce long periods to cleverly piece together without concrete.
Pozzolan is used today, generally as an additive. Note that fly ash is similar (http://www.ctlgroup.com/lab-services/lab-tests/astm-c-618-co...). Again because of the long cure time the original Roman concrete is not in favor, but you may achieve the performance you need through the use of an admixture.
I should add that some of these recent articles may be linked to the general business interest in the increased use of pozzolanic admixtures, since there is a ready source in fly ash and also some parts of the world have vast amounts of pozzolanic ash ready to be exploited.