In this chapter sixty years of history of machine translation research and development is reviewed, concentrating on the essential difficulties and limitations of the task, and how the various approaches have attempted to solve, or more usually work around, these. The chapter focuses on how computational linguists have addressed translation as a problem, and assumes in the reader a general familiarity with computers from the point of view of users, without going into unwarranted detail about the specifics of the programs that have been developed.