Climate change is a continuous spatiotemporal reality, possibly endangering the viability of the grapevine (Vitis vinifera L.) in the future. Europe emerges as an especially responsive area where the grapevine is largely recognised as one of the most important crops, playing a key environmental and socio-economic role. The mounting evidence on significant impacts of climate change on viticulture urges the scientific community in investigating the potential evolution of these impacts in the upcoming decades. In this review work, a first attempt for the compilation of selected scientific research on this subject, during a relatively recent time frame (2010–2020), is implemented. For this purpose, a thorough investigation through multiple search queries was conducted and further screened by focusing exclusively on the predicted productivity parameters (phenology timing, product quality and yield) and cultivation area alteration. Main findings on the potential impacts of future climate change are described as changes in grapevine phenological timing, alterations in grape and wine composition, heterogeneous effects on grapevine yield, the expansion into areas that were previously unsuitable for grapevine cultivation and significant geographical displacements in traditional growing areas. These compiled findings may facilitate and delineate the implementation of effective adaptation and mitigation strategies, ultimately potentiating the future sustainability of European viticulture.