Fuel is injected into the compressed air stream, vaporized, and burned. Typical fuel to air ratios are as low as 1:60 (vs 1:14 of stoichiometric) and flame stabilization is difficult.
The compressor exit flow is diffused and divided into the primary and secondary flows. Since conventional flame velocities are low the primary flow is swirled and fuel is injected to provide the recirculation to stabilize the flame.
The burning area is enclosed by a perforated liner which assists in directing the flame and provides a heat shield for the surrounding structure. The chamber liner is cooled by the secondary air which subsequently mixes with the burning primary flow and cools the burnt gases to the required temperature.
The early combustion chambers were "can" shaped, and needed individual ignition sources and tuning.
The intermediate design was can-annular or cannular which connected the individual can chambers and provided better uniformity of combustion.
Annular combustors have a more compact axisymmetric design with only the swirl vanes and injector nozzles locating the primary flame positions. Annular designs are more space and energy efficient.
Reverse flow and straight flow 
Understanding of combustion processes has allowed the development of smokeless combustors.
Annular combustors with dual injection rings are used in engines such as the GE90. Both annuluses are lighted for take off thrust. Under lighter loads such as cruise only one row operates.
An afterburner (or reheat) is a combustor located immediately upstream of the engine final nozzle, where fuel is burnt to raise the nozzle entry gas temperature, thereby increasing the net thrust of the engine. Because of the relatively high fuel consumption associated with afterburning, the system has to be used sparingly. A variable area nozzle is normally fitted to accommodate the increased gas volume flow when the afterburner is alight. Increasing the nozzle area enables a satisfactory compression match to be maintained, as nozzle temperature is increased. Afterburning is used mainly on military aircraft to reduce take-off roll and to overcome the additional drag encountered when the aircraft is flying at transonic and supersonic conditions. Concorde, the supersonic airliner, also incorporated engine afterburning, but the system was unlit at supersonic cruise, which considerably enhanced the aircraft's range.