This work deals with the optimization of Deep Convolutional Neural Networks (ConvNets). It elaborates on the concept of Adaptive Energy-Accuracy Scaling through multi-precision arithmetic, a solution that allows ConvNets to be adapted at run-time and meet different energy budgets and accuracy constraints. The strategy is particularly suited for embedded applications made run at the “edge” on resource-constrained platforms. After the very basics that distinguish the proposed adaptive strategy, the paper recalls the software-to-hardware vertical implementation of precision scalable arithmetic for ConvNets, then it focuses on the energy-driven per-layer precision assignment problem describing a meta-heuristic that searches for the most suited representation of both weights and activations of the neural network. The same heuristic is then used to explore the optimal trade-off providing the Pareto points in the energy-accuracy space. Experiments conducted on three different ConvNets deployed in real-life applications, i.e. Image Classification, Keyword Spotting, and Facial Expression Recognition, show adaptive ConvNets reach better energy-accuracy trade-off w.r.t. conventional static fixed-point quantization methods.