Solar sailing is emerging as a promising form of advanced spacecraft propulsion, which can enable exciting new space-science mission concepts. By exploiting the momentum transported by solar photons, solar sails can perform high-energy orbit-transfer manoeuvres without the need for reaction mass. Missions such as planetary-sample return, multiple small-body rendezvous and fast missions to the outer Solar System can therefore be enabled with the use of only a modest launch vehicle. In addition, new families of highly non-Keplerian orbits have been identified that are unique to solar sails, and can enable new ways of performing space-science missions. While the opportunities presented by solar sailing are appealing, engineering challenges are still to be solved before the technology finally comes to fruition.