[en] It is possible to explain the gross features of extensive air showers using very different alternative assumptions about the character of particle interactions, provided that different assumptions are made about the primary particle flux and composition. From this fact it is first shown that a very consistent set of fairly direct measurements on primary flux now exists (subject to the acceptance of a systematic bias in one set of data), together with constraints on the composition. (Protons and other nuclei however turn out not to have the same rigidity spectrum.) The gross features of showers mostly fit a scaling model with rising cross sections, but there are contrary indications (particularly from γ -ray flux, particle spread and core structure at the higher energies) that a change in the nature of interactions occurs above 10¹⁵eV, and this puzzle has not been solved