The ability of climbing plants to grow upward along others to reach the canopy for photosynthesis is hypothesized as a key innovation in flowering plants. Most members of the Cucurbitaceae, a family containing ∼1000 species and many important crops, are climbers and have characteristic tendrils and pepo fruits. Here, we present 127 newly sequenced transcriptomes and genomes along with other datasets for a total of 136 cucurbits representing all tribes to establish a robust Cucurbitaceae phylogeny containing eight highly resolved major clades. We analyzed whole-genome duplication, diversification dynamics, and ancestral morphologies, and found that after early genome duplication event(s), a burst of diversification and morphological innovations in flower, fruit, and root characters occurred under the climate optimum in the Early Eocene. Species radiation during the Mid-Eocene Climatic Optimum also coincided with several morphological changes shared by 80% of cucurbits. We found that the cucurbit-specific tendril identity gene TEN originated from a paleo-polyploidization event at the origin of the family. Our results support the hypothesis that cucurbit diversifications were probably driven by increased genetic diversity following polyploidizations and by trait morphological innovations under paleo-climate upheavals. Our study provides a phylogenetic framework and new insights into morphological and genomic changes underlying the adaptive evolution of Cucurbitaceae.