In recent years, signal processing applications that deal with user-related data have aroused privacy concerns. For instance, face recognition and personalized recommendations rely on privacy-sensitive information that can be abused if the signal processing is executed on remote servers or in the cloud. In this tutorial article, we introduce the fusion of signal processing and cryptography as an emerging paradigm to protect the privacy of users. While service providers cannot access directly the content of the encrypted signals, the data can still be processed in encrypted form to perform the required signal processing task. The solutions for processing encrypted data are designed using cryptographic primitives like homomorphic cryptosystems and secure multiparty computation (MPC).