The processing and encryption of multimedia content are generally considered sequential and independent operations. In certain multimedia content processing scenarios, it is, however, desirable to carry out processing directly on encrypted signals. The field of secure signal processing poses significant challenges for both signal processing and cryptography research; only few ready-to-go fully integrated solutions are available. This study first concisely summarizes cryptographic primitives used in existing solutions to processing of encrypted signals, and discusses implications of the security requirements on these solutions. The study then continues to describe two domains in which secure signal processing has been taken up as a challenge, namely, analysis and retrieval of multimedia content, as well as multimedia content protection. In each domain, state-of-the-art algorithms are described. Finally, the study discusses the challenges and open issues in the field of secure signal processing.