Most radial engines were replaced by turboprops. The very large R-4360, R-3350, and R-2800engines were directly replaced by larger turboprop engines like the T-34 and 501D (T-56), while the aircraft that used them (the Boeing C-97/377, the Lockheed Constellation, the DC-7 and DC-6) were replaced by turbojet powered aircraft like the KC-135, the 707, the DC-8 ect.
The smaller radials like the R-1820, the R-1830, the R-1340, and the R-985 went on for a bit longer and many are still in service today.. but most have been replaced by smaller turboprop engines like the PT6 and TPE-331s.
At the very low end... opposed engines have proven themselves much superior. Opposed engines are compact and have a low frontal area, they have a simple wet sump oil system, they have a camshaft instead of a complex set of cam rings and planetary gears, as well as a simple crankshaft and con rods that produce even timing vs a massive single throw crank with master and articulating rods which produce uneven timing, and they don't suffer from hydraulic lock or leaking oil from the inverted cylinders.
There is a company out of Australia called Rotec that makes small (>200hp) radials for homebuilts but it is mostly for a nostalgic look and sound... as the aircraft's performance degrades considerably in comparison to other engines.