Integrated sensing and communication (ISAC) technology is one of the featuring technologies of the next-generation communication systems. When sensing capability becomes ubiquitous, more information can be collected, which can facilitate many applications in intelligent transportation, unmanned aerial vehicle (UAV) surveillance and healthcare. However, it also faces many information privacy leakage and security issues. This article highlights the potential threats to privacy and security and the technical challenges to realizing private and secure ISAC. Three promising combating solutions including artificial intelligence (AI)-enabled schemes, friendly jamming and reconfigurable intelligent surface (RIS)-assisted design are provided to maintain user privacy and ensure information security. Case studies demonstrate their effectiveness.