The notion of NP-completeness has provided a (66) mathematical definition for (67) intractability of NP problems.But this measure applies only to worst-case complexity.Being NP-complete does not (68) that a problem is intractable on the average case. Indeed, some NP-complete problems are " (69) on average", though some may not be. Levin initiated the study of average-case intractability, He showed that a bounded tiling problem under a simple distribution is average-case NP-complete. Since then, several additional average-case NP-complete problems have been shown within Levin’s (70) . This paper is intended to provide a comprehensive survey of average-case NP-complete problems that have been published so far, and the techniques of obtaining these results.