The survey addresses recent work that has the aim of preserving privacy in speech communication applications. The talk discusses recent privacy legislation in the US and especially the European Union, and focuses upon the GDPR (EU Regulation 2016/679) and the Police Directive (EU Directive 2016/680), covering also ‘Privacy by Design’ and ‘Privacy by Default’ policy concepts. Emphasis is placed on voice biometrics and non-biometric speech technology. Since there is no “one size fits all” solution, specific cryptographic solutions to privacy preservation are highlighted. Among other classification tasks, voice biometrics can intrude on privacy when misused; the talk surveys a number of privacy safeguards. The international standard for biometric information protection is reviewed and figures of merit are proposed regarding, e.g., the extent to which privacy is preserved. More interdisciplinary efforts are necessary to reach a common understanding between speech technology, legislation, and cryptography communities (among many others). Future challenges include the need to not only carry out decision inference securely, but also to preserve privacy, where cryptographic methods need to meet the demands of speech signal processing. In communication, speech is a medium, not a message.