A rotary internal combustion engine includes an outer housing and an inner housing and an enclosure defined therebetween. At least one of the outer and inner housings is rotatable relative to the other and at least two barriers are disposed in the enclosure and divide the enclosure into a combustion chamber and an exhaust chamber. At least one barrier is rotatable relative to at least one other barrier and at least one barrier comprises a retractable barrier mounted along a pivot axis and is pivotable between an extended position and a retracted position. An intake port, exhaust port, and ignition source are also provided. A method of combusting a fuel comprises rotating a drive member to expand a combustion chamber and substantially isolate the combustion chamber from an exhaust chamber, and introducing and combusting a combustion fluid and a fuel in the combustion chamber as the combustion chamber is expanding.