Main advantages over conventional piston/cylinder engines:

larger inlet port opening (more than 4x larger than reciprocating) 
higher gas flow, higher volumetric efficiency, lower pumping losses
higher speeds, lower NOx, higher specific power
high swirl on entry, swirl increasing during compression, faster combustion, higher efficiency
almost constant flow, low inertia inlet/exhaust

lower weight, compact, simple
lower part count, no valve train, no camshaft, no gears
3 main moving parts for 4 main combustion chambers
4 stroke engine at 4 combustions per crank rotation
higher specific power maintaining proper sealing, lubrication and cooling

exposed rotor area increases as combustion pressure drops
almost constant torque
flat sinusoidal volume change, more available combustion time at TDC, higher efficiency
almost constant combustion force on bearings
robust, simple to manufacture, large tolerance shapes, low maintenance

simple integration of variable compression
cost effective flex-fuel and fuel efficiency optimisation, lower CO2 emissions
controlled auto ignition (HCCI) enabled
space for additional valves/injectors/spark plugs (EGR, Miller, etc)
4 secondary chambers for additional pumping, cooling or power

simple to cool, lubricate and seal
no wiping of oil into the exhaust port
cooling directly through the piston and other parts
continuous contact of side and top seals, back pressured by compression gasses
higher operating temperatures