In contrast to ion beams produced by conventional accelerators, ion beams accelerated by ultrashort intense laser pulses have advantages of ultrashort bunch duration and ultrahigh density, which are achieved in compact size. However, it is still challenging to simultaneously enhance their quality and yield for practical applications such as fast ion ignition of inertial confinement fusion. Compared with other mechanisms of laser-driven ion acceleration, the hole-boring radiation pressure acceleration has a special advantage in generating high-fluence ion beams suitable for the creation of high energy density state of matters. In this paper, we present a review on some theoretical and numerical studies of the hole-boring radiation pressure acceleration. First we discuss the typical field structure associated with this mechanism, its intrinsic feature of oscillations, and the underling physics. Then we will review some recently proposed schemes to enhance the beam quality and the efficiency in the hole-boring radiation pressure acceleration, such as matching laser intensity profile with target density profile, and using two-ion-species targets. Based on this, we propose an integrated scheme for efficient high-quality hole-boring radiation pressure acceleration, in which the longitudinal density profile of a composite target as well as the laser transverse intensity profile are tailored according to the matching condition.