Thermoacoustics exploit a temperature gradient to produce powerful acoustic pressure waves. The technology has a key role to play in energy harvesting systems. A time-line in the development of thermoacoustics is presented from its earliest recorded example in glass blowing through to the development of the Sondhauss and Rijke tubes to Stirling engines and pulse-tube cryo-cooling. The review sets the current literature in context, identifies key publications and promising areas of research. The fundamental principles of thermoacoustic phenomena are explained; design challenges and factors influencing efficiency are explored. Thermoacoustic processes involve complex multi-physical coupling and transient, highly non-linear relationships which are computationally expensive to model; appropriate numerical modelling techniques and options for analyses are presented. Potential methods of harvesting the energy in the acoustic waves are also examined.