Three applications of free-piston engines are considered: (a) An internal-combustion engine air compressor combination where the useful output is compressed air for pneumatic purposes. (b) An air compressor combustion-chamber combination for the production of hot gases under pressure for use in a turbine to produce shaft work. (c) The compressor system as described in (a) together with a combustion chamber for internal-combustion heating of the compressed air and then a turbine to utilize the hot gases for the production of shaft work. Performance data for several existing free-piston systems are presented together with the results of cycle studies. The thermodynamic-dynamic design aspects are considered relative to the conventional crank-type reciprocating internal-combustion-engine system. The general conclusion reached is that the free-piston system has the prime advantages of excellent thermodynamic performance combined with mechanical simplicity. Consequently, a major development effort appears to be well warranted.