With the rapid development of cloud computing, the enterprises and individuals can outsource their sensitive data into the cloud server where they can enjoy high quality data storage and computing services in a ubiquitous manner. This is known as the outsourcing computation paradigm. Recently, the problem for securely outsourcing various expensive computations or storage has attracted considerable attention in the academic community. In this book, we focus on the latest technologies and applications of secure outsourcing computations. Specially, we introduce the state-of-the-art research for secure outsourcing some specific functions such as scientific computations, cryptographic basic operations, and verifiable large database with update. The constructions for specific functions use various design tricks and thus result in very efficient protocols for real-world applications. The topic of outsourcing computation is a hot research issue nowadays. Thus, this book will be beneficial to academic researchers in the field of cloud computing and big data security.