Veri able computation is an important mechanism for ensuring the soundness (reliability) of func-tion evaluation results produced when delegating computation in distributed computing or cloud computing. We summarize the important achievements about veri able computation, in particular, from the perspectives of cryptography and computational theory. For veri able computation in computational theory, we summarize the connection between interactive proofs, PCP theorems, and CS proofs and describe their development and applications. With regard cryptography, we discuss the state-of-the-art veri able computation schemes that were constructed by applying cryptography tools. In addition, we survey veri able computation schemes in the out-sourced storage setting. Finally, we conclude with a discussion on the future development direction for veri able computation.