I have studied Roman concrete for many years in all aspects down to the molecular. It was an impressive use of technology for it's time, but there is no mystery to it. The particular advantages that it had have been adapted for modern use:
It was naturally hydraulic, which simply means that it will set under water. During the time Roman concrete was used, the volcanic pozzolan was the most common hydraulic known, but others were known and used (naturally hydraulic limes were used concurrently in the area of today's France, for example).
The pozzolans act as both a plasticizer and a water-reducer (as does lime, hydraulic or not).
Salt water could be used to mix it (we have not pushed this aspect since we generally use rebar or other metal reinforcing and they do not play well with excess salts, but normal portland cement can be used in salt water concrete with no other issues).