I found an old port of Firefox but its support for more modern language features was lacking.
As I understand it, there are 2 modern browsers in development for RISC OS.
Iris is a new native program.
The other is OWB, based on the Otter browser. This is a port, so not a native app, however it is a little more mature.
Both are based on the Webkit engine.
There are new browsers coming, one of which is based on webkit, the details where released at the Wakefield riscos user show last weekend (April 27th 2019), I can't recall the name, but it's getting released to trade and investors first, and then a while later it will hit the public.
You can find the full report for the most recent show on "iconbar.com" :
(PS: If you look in the pictures from the show, I'm hovering around in some of them, I was down at the 8-bit end of the hall with ABug/Stardot and the rest of the BBC crowd) :-)
(PPS: You may also want to come and join the stardot forums: https://stardot.org.uk/forums/index.php pretty much anyone whos involved in the Acorn/BBC/Archimedies/RiscOs/rPI scene is a member there)