We discuss the problem of privacy in autonomous systems, introducing different conceptualizations and perspectives on privacy to assess the threats that autonomous systems may pose to privacy. After this, we outline socio-technical and legal measures that should be put in place to mitigate these threats. Beyond privacy threats and countermeasures, we also argue how autonomous systems may be, at the same time, the key to address some of the most challenging and pressing privacy problems nowadays and in the near future.