The Particle Flow (PFlow) approach to calorimetry promises to deliver unprecedented jet energy resolution for experiments at future high energy colliders such as the proposed International Linear Collider (ILC). This paper describes the PandoraPFA particle flow algorithm which is then used to perform the first systematic study of the potential of high granularity PFlow calorimetry. For simulated events in the ILD detector concept, a jet energy resolution of σ E / E ≲ 3.8 % is achieved for 40–400 GeV jets. This result, which demonstrates that high granularity PFlow calorimetry can meet the challenging ILC jet energy resolution goals, does not depend strongly on the details of the Monte Carlo modelling of hadronic showers. The PandoraPFA algorithm is also used to investigate the general features of a collider detector optimised for high granularity PFlow calorimetry. Finally, a first study of the potential of high granularity PFlow calorimetry at a multi-TeV lepton collider, such as CLIC, is presented.