With the advent of multi-petawatt lasers, the relativistic transparency regime of laser-plasma interactions becomes readily accessible for near-solid density targets. Initially opaque targets that undergo relativistic self-induced transparency (RSIT) have already shown to result in promising particle acceleration and radiation generation mechanisms, as well as relativistic optical and photonics phenomena that modify the spatial, temporal, spectral and polarization properties of the laser pulse itself. At the maximum laser intensities currently available, this opaque-to-RSIT transition regime can be achieved through ultrafast ionization, heating and expansion of initially ultrathin foil targets. Here, we review findings from our programme of work exploring this regime experimentally and numerically, including changes to the laser energy absorption, mechanisms for laser-driven particle acceleration and the generation of a relativistic plasma aperture. New physics induced by this aperture, such as the production of intense light with higher order spatial modes and higher harmonics, and spatially-structured and temporally-varying polarization states, is summarized. Prospects for exploring the physics of the RSIT regime with higher intensity and high repetition rate lasers, including expected new phenomena such as high-field effects and the application of new techniques such as machine learning, are also discussed; outlining directions for the future development of this promising laser-plasma interaction regime.