With　the　ever-increasing　requirement　of　storage　and　computation　resources,　it　is　unrealistic　for　local　devices　(with　limited　sources)　to　implement　large-scale　data　processing.　Therefore,　individuals　or　corporations　incline　to　outsource　their　computation　requirements　to　the　cloud.　However,　data　outsourcing　brings　security　and　privacy　concerns　to　users　when　the　cloud　servers　are　not　fully　trusted.　Recently,　extensive　research　works　are　conducted,　aiming　at　secure　outsourcing　schemes　for　diverse　computational　tasks　via　different　technologies.　In　this　survey,　we　provide　a　technical　review　and　comparison　of　existing　outsourcing　schemes　using　diverse　secure　computation　methods.　Specifically,　we　begin　the　survey　by　describing　security　threats　and　requirements　of　secure　outsourcing　computation.　Meanwhile,　we　introduce　four　secure　techniques　(i.e.,　secure　multi-party　computation,　pseudorandom　functions,　software　guard　extensions,　and　perturbation　approaches)　and　their　related　works.　Then,　we　focus　on　the　theories　and　evolution　of　homomorphic　encryption,　as　well　as　the　applications　of　the　basic　operations　and　application-specific　tasks.　Finally,　we　discuss　the　security　and　performance　of　existing　works　and　give　future　directions　in　this　field.　©　2013　IEEE.