An Overview of the Sieve Method and its History

This is a revised version of NT0505521, a translation of our Japanese expository article that was published under the title `{\it An overview of sieve methods}' in the second issue of the 52nd volume of Sugaku, the Mathematical Society of Japan, April 2005. A number of textual improvements are incorporated, for which the author is grateful to G. Greaves of Cardiff University, UK. Also, a new addendum is added for the sake of updating.