  The future applications of the short-duration, multi-MeV ion beams produced
in the interaction of high-intensity laser pulses with solid targets will
require improvements in the conversion efficiency, peak ion energy, beam
monochromaticity, and collimation. Regimes based on Radiation Pressure
Acceleration (RPA) might be the dominant ones at ultrahigh intensities and be
most suitable for specific applications. This regime may be reached already
with present-day intensities using circularly polarized (CP) pulses thanks to
the suppression of fast electron generation, so that RPA dominates over sheath
acceleration at any intensity. We present a brief review of previous work on
RPA with CP pulses and a few recent results. Parametric studies in one
dimension were performed to identify the optimal thickness of foil targets for
RPA and to study the effect of a short-scalelength preplasma. Three-dimensional
simulations showed the importance of ``flat-top'' radial intensity profiles to
minimise the rarefaction of thin targets and to address the issue of angular
momentum conservation and absorption.
