Viticulture has been an important economic sector for centuries. In recent decades, global wine production has fluctuated between 250 and almost 300 million hectoliters, and in 2022, the value of wine exports reached EUR 37.6 billion. Climate change and the associated higher temperatures could favor the occurrence of ochratoxin A (OTA) in wine. OTA is a mycotoxin produced by some species of the genera Aspergillus and Penicillium and has nephrotoxic, immunotoxic, teratogenic, hepatotoxic, and carcinogenic effects on animals and humans. The presence of this toxin in wine is related to the type of wine—red wines are more frequently contaminated with OTA—and the geographical location of the vineyard. In Europe, the lower the latitude, the greater the risk of OTA contamination in wine. However, climate change could increase the risk of OTA contamination in wine in other regions. Due to their toxic effects, the development of effective and environmentally friendly methods to prevent, decontaminate, and degrade OTA is essential. This review summarises the available research on biological aspects of OTA prevention, removal, and degradation.