While wine is inherently acceptable to drink for those who keep kosher, owing to the specialness of wine in the Jewish tradition, there are some unique parameters for its fitness of consumption, kashrut.
The issue of gentile wine is the most significant limiting parameter around the kashrut of wine. While there are biblical agricultural commandments that limit certain foods for harvesting (e.g. orlah and others), this is perhaps the central concern when it comes to the kashrut of wine these days. In order for a wine to be kosher, it does not require the blessing of rabbis or anyone else for that matter. The primary concern is that wine, at least from the time that the grapes are crushed until the wine is pasteurized, that no gentiles come into contact with it.
The origins of the concerns of wine coming to contact with gentiles goes back to Talmudic times by the rabbis. The central concern for the rabbis was not to consume any wine that was used for idolatrous purposes (יין נסך), whether this wine was actually used for idolatrous libations or in the process of being used for such, even the wine having been touched by an idolater would would send such wine into the category of this idolatrous libation wine and make it totally off limits for either Jewish consumption or even Jewish possession or selling. For more on this topic, see The Jewish Drinking Show, episode #71.
The rabbis also created a second prohibition with regards to gentile wine, which was regular gentile wine that was not used for idolatrous purposes (סתם יינם). They considered even just this standard gentile wine as problematic, not due to any inherent problem with the wine, but rather that it could cause intermarriage with gentiles. Not only was drinking gentile wine seen to be problematic, but even selling it was considered to be off-limits.
As there were significantly fewer idolaters in the Medieval ages, the concern regarding idolatrous libation wine greatly lessened and there were even medieval rabbinic authorities who created leniencies with regards to this gentile wine, since they were less concerned about idolatry amongst their gentiles and began permitting owning and selling even gentile wine.
While the concern of the use of wine for idolatrous libations is significantly less so than it was many centuries ago for the rabbis of the Talmudic era, nevertheless, the concern around intermarriage with gentiles still remains and, as such, the consumption of gentile wine is still forbidden for normative Jewish practice, while possession of and selling of gentile wine is largely permitted.