Strong-field quantum electrodynamics predicts electron-seeded electron-positron pair cascades when the electric field in the rest-frame of the seed electron approaches the Sauter-Schwinger field, i.e. h =Ẽ E 1 S RF . Electrons in the focus of next generation multi-PW lasers are expected to reach this threshold. We identify three distinct cascading regimes in the interaction of counter-propagating, circularly-polarised laser pulses with a thin foil by performing a comprehensive scan over the laser intensity (from 10 23 to 5×10 24 W cm −2 ) and initial foil target density (from 10 26 to 10 31 m −3 ). For low densities and intensities the number of pairs grows exponentially. If the intensity and target density are high enough the number density of created pairs reaches the relativistically-corrected critical density, the pair plasma efficiently absorbs the laser energy (through radiation reaction) and the cascade saturates. If the initial density is too high, such that the initial target is overdense, the cascade is suppressed by the skin effect. We derive a semi-analytical model which predicts that dense pair plasmas are endemic features of these interactions for intensities above 10 24 W cm −2 provided the target's relativistic skin-depth is longer than the laser wavelength. Further, it shows that pair production is maximised in near-critical-density targets, providing a guide for near-term experiments.S RF . We can reach η∼1 for laser fields much weaker than E S as the fields themselves can rapidly accelerate electrons to high Lorentz factor, resulting in a strong Lorentz boost to E RF . Pair production by the multi-photon Breit-Wheeler process can occur if the photons emitted during Compton scattering satisfy a similar condition on their quantum efficiency parameter (defined below) χ∼1. An electromagnetic cascade can ensue if many generations of electrons and positrons can be generated by the fields. Usually this occurs via a two-step process whereby the electrons and positrons produced by the Breit-Wheeler process radiate photons by nonlinear Compton scattering which subsequently decay to further pairs and so on.Upcoming facilities, like several of those comprising the extreme light infrastructure (ELI) [1,2], are expected to reach laser intensities of > -