Using encryption anyone can securely store data on the cloud. While this provides clear benefits, it also has some significant drawbacks. For instance, it is commonly believed that encrypted data cannot be manipulated without first being decrypted, making the encrypted data static. Therefore a fundamental question arises: Can we process encrypted data without having to decryot it first? In this talk, we will try to answer this question in a variety of settings, exploring one of the most exciting research areas in cryptography