New sensor technologies are under development to cope with the ever increasing requirements for high energy physics (HEP) detectors. For the High-Luminosity LHC (HL-LHC) and the Future Circular Collider (FCC) higher radiation hardness, improved timing performance and lower cost large area detector technologies are essential. Recent developments of p-type silicon planar sensors, sensors with intrinsic gain for timing applications and monolithic sensors are examples for next generation detector technologies. A commonality of these new sensors is the use of boron doped p-type silicon, while present HEP sensors are essentially based on n-type silicon. Consequently, radiation effects in p-type silicon have been less studied in the detector community, but are now of high relevance. In this paper, we review radiation effects in p-type silicon devices with a focus on acceptor removal effects. In p-type silicon exposure to radiation causes an apparent deactivation of the dopant. This so-called acceptor removal effect is for example evidenced by an initial decrease of depletion voltage in p-type sensors with rising particle fluence, while after exposure to higher fluences the device behavior is dominated by other radiation induced effects. Low Gain Avalanche Detectors (LGADs) are the baseline technology for future solid-state timing layers at the HL-LHC. Their good timing performance is based on the intrinsic amplification of the signal by impact ionization in a highly doped p-type gain layer. Radiation effects reduce the active boron concentration in the gain layer and lead to a reduction in field strength and consequently a loss of intrinsic signal amplification, thus limiting the radiation hardness of this technology. Monolithic detectors, especially High Voltage CMOS, are another technology affected by acceptor removal, as the bulk silicon used for the sensor is typically of p-type. We review the impact of radiation damage on the depleted volume as function of the initial boron concentration and the corresponding chang...