Wine holds a special place in Jewish law because it was used in the libations of ancient idol worship. Scripture speaks of the wine of drink offerings, and the Mishnah and Talmud, in tractate Avodah Zarah, forbid wine poured for an idol, yayin nesech.
The sages extended the prohibition to ordinary wine, stam yeinam, handled by anyone who does not observe Shabbat and kashrut according to Orthodox tradition, whether or not any rite was involved. In the classical sources the decree concerned wine handled by people of other faiths; today's practice defines it by observance. That is why the requirements for kosher wine concern people rather than grapes: from the moment the liquid is separated from the solids until the wine is pasteurised or the bottle is sealed, it may be handled only by Sabbath-observant Jews.
The main exception is mevushal, cooked wine, which is regarded as unfit for idolatrous use and so is not subject to the prohibition. Authorities disagree on the temperature required, with positions ranging from about 74 to 90 °C. In practice mevushal wine is made by flash pasteurisation, and once it is mevushal anyone may pour it, which is why caterers and restaurants ask for it.
The components of wine itself, alcohol, sugars, acids and phenolic compounds, raise no kashrut questions. The problems lie in processing aids, above all animal-derived fining agents, which must be kosher or replaced by mineral and plant alternatives.
This page explains the background only. Questions of practice at a particular winery are decided by the certifying body and its rabbis.
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