A furnace for burning solid fuel in pieces has a horizontal mechanically operated grate (7) for supporting and advancing a burning fuel bed. Primary and secondary air channels (11) and (12) are formed in the grate to pass airflows up through the fuel bed. Fuel (29) is delivered directly onto a fuel-receiving surface (26) of the grate (7) from a rotary feeder drum (30), which forms an air seal, down a steeply inclined chute (50). Additional air is blown in under pressure to the space above the primary air channels (11) to cause turbulence and assist in burning volatile components given off by the fuel.