Cryptographic operations are performed everywhere, from standard laptop to smart cards. Some devices computational resources can be very limited and it is natural to delegate costly operations to another device capable of carrying out cryptographic algorithms. In this setting, it is obviously important to ensure the limited device that the computation is carried out correctly and that the powerful device does not learn anything about what is actually computing (including the secret inputs and outputs). We briefly review the recent advances on secure outsourcing of group exponentiation (in groups of known prime order as well as in groups of unknown order) and pairing computation.