Part 1 A long overdue re-appraisal: The famous engine that never was; What Carnot efficiency? The counter-flow spiral heat exchanger – Spirex; A high-recovery-ratio combustion chamber. Part 2 Living with incompressible flow data: The regenerator problem brought down to size; The regenerative annulus and shuttle heat transfer; The rotating-displacer air engine; The strange case of the self-regulating air engine; Some light on the inner workings of the thermal lag engine. Part 3 Working with the reality of compressible flow: New correlations for old; Regenerator thermal analysis – un-finished business; Flow passage geometry; Beyond the performance envelope; For the sceptics. Part 4 Some design considerations: Scaling - and the neglected art of back-of-the-envelope calculation. 'How to make a business out of Stirling Engines today'.