Aim The Caucasus is a global biodiversity hotspot that includes a wide diversity of temperate forests, from xeric to mesic and rain forest. Little is known about their vulnerability to climate change. We aimed to identify the major climate constraints on tree growth. Location Western Caucasus of Georgia, Russia and Turkey (40–43° N, 41–43° E). Time period Twentieth century. Major taxa studied Trees, angiosperms and gymnosperms. Methods We used a new network of 35 tree‐ring width chronologies from four angiosperm and four gymnosperm species across an elevational gradient of > 2,000 m. We used correlations to identify the major climate factors (temperature, precipitation and drought) at monthly and seasonal scales affecting tree growth and to assess whether their effects change over time. To explore common response patterns among species, we used self‐organizing maps, a type of artificial neural network. Results Spring or summer drought reduced radial growth of most tree species, despite large differences in elevation. As expected, drought was particularly detrimental at warm, low‐elevation sites. Besides drought, growth of conifers at high elevations was also limited by cold winters and summers. Important species‐specific climate–growth responses were also evident. In general, climate–growth relationships were stable over time, except at some cold‐limited sites, where positive responses to summer and winter temperatures have diminished over the last few decades. Main conclusion Growth responses to precipitation and drought among species were more similar than they were to temperature, even at humid sites, providing further evidence of drought vulnerability in mesic forests. The productivity of high‐elevation conifer forests, limited by summer drought and low temperatures, will depend on the balance between temperature and precipitation. Given that climate change is expected to induce larger climatic gradients in the region, the potential reduction of forest cover at a regional scale would make the conservation of these mesic forests more essential.