Augustus is an open source game engine re-implementation for Caesar III, forked from another called Julius that aims to add in new features.
Version 3.1 is out now adding in plenty of new goodies like: a volume slider, a Hippodrome betting system, roofed garden walls, palisades for cheaper walls, a new difficulty option to adjust the max number of allowed grand temples per city, new hotkeys, resource stockpiling is now an option to production buildings and warehouses, an option to have number separators for larger numbers and many more improvements and bug fixes. It's making it easily one of the best ways to play the classic city-builder.
You do need the original game assets, which you can grab easily with a DRM-free copy of Caesar III on GOG.com or Steam. Find the project on GitHub. You can also play it easily from Steam using Luxtorpeda!
Something else worth keeping an eye on is Ozymandias, which aims to do the same thing for Pharaoh, using the base game engine from Julius and Augustus. I'll be following that one along with great interest!