We present a detailed single pulse study of PSR B1055–52 based on observations at the Parkes radio telescope. The radio emission is found to have a complex modulation dominated by a periodicity of ∼20 times its rotational period P (0.197 s), whose phase and strength depends on pulse longitude. This periodicity exhibits a phase-locked delay of about 2.5P between the main pulse (MP) and interpulse (IP), presumed to be the opposite poles of the pulsar. This delay corresponds to a light-travel distance of many times the light-cylinder radius. More complex modulations are found within the MP on time-scales down to about 9P, and both these and the principal modulation vary strongly across the (at least) seven components which the MP and IP exhibit. The nature of the single pulse emission, which ranges from smooth and longitudinally extended to ‘spiky’, is also component-dependent. Despite these disparities, the total pulse intensity distributions at the MP and IP are virtually identical in shape, suggesting a common emission mechanism. In an attempt to account for the complex modulations, we examine a number of physical models, both intrinsic (which presuppose the pulsar to be an isolated neutron star) and extrinsic (appealing to the presence of circumstellar material to modulate the emission). Significant objections can be made to each model, so this pulsar’s behaviour patterns remain a crucial challenge to theorists.