The interaction of ultra-high intensity laser pulses with solid targets is studied theoretically and with Particle- In-Cell (PIC) simulations. The regime of Radiation Pressure Acceleration of ultrathin foil targets is investigated within an improved "Light Sail" or "accelerating mirror" model. The latter provides simple and useful scalings for the characteristics of accelerated ions. The underlying dynamics, unfolded by PIC simulations, is however more complex than the simple model may suggest. An important issue is the heating of electrons that, even if strongly reduced by the use of circulary polarized (CP) pulses, may lead to a significant broadening of the ion spectrum. Radiation Reaction (RR) effects in the ultra-relativistic regime of extreme intensities are included in the PIC simulations via the Landau-Lifshitz formula. Apparently, for linearly polarized pulses RR slightly reduces the ion energy but also contributes to cooling the electrons, while RR effects are rather weak for CP pulses.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.