The standard before the popularization of turbine engines, radial engines cylinder engines "radiate" out from the center through a reciprocating type of internal combustion. They dominated the skies for more than half a century by their ability to self-air-cool, and the sheer power they produced.
The Continental radial engine was commonly used during the 1930s and into WWII---the very engine used in some of the aircrafts we use, such as the Stearman or Waco. The Jacobs radial was developed in 1933 and was still in use well into the 1970s.
The first radial engine was constructed in 1901, with 5 water-cooled cylinders. Cooling problems common with the early water-cooled versions were solved once the engine itself could generate its own cooling airflow, accomplished by no longer bolting the propeller to the engine, and the crankshaft to the air frame. By 1907, the first standard, air-cooled version was developed by Jacob Ellehamme, drawing from his experience working with motorcycles--Harley Davidsons run on radial engines. The Azrani was another early version, and was even used for the first air crossing of the English Channel.
But it took almost a decade for the radial engine to be considered trustworthy for flying. Support was boosted from the National Advisory Committee for Aeronautics's 1921 declaration that radials were more reliable and efficient, and the U.S. Navy's decision the year after to purchase only aircrafts fitted with air-cooled radials. Aluminum cylinders with steel liners were modified, providing radial engine's reliability on long-range flights over water. The J-5 radial engine was even used for the first solo, trans-Atlantic flight. By WWII, radial engines had fully replaced rotary engines as the standard and provided much of the aircraft power. The demand for faster and higher flying eventually replaced them for jet engines. Radial engines are still in use in old aircrafts.