To address functional-output regression, we introduce projection learning, a novel dictionary-based approach that learns to predict a projection of the output function on a dictionary while minimizing a functional loss. Projection learning makes it possible to use non orthogonal dictionaries and can then be combined with dictionary learning. It is thus much more flexible than expansion-based approaches relying on vectorial losses. Using reproducing kernel Hilbert spaces of vector-valued functions, this general method is instantiated as kernel-based projection learning (KPL). For the functional square loss, we propose two closed-form estimators, one for fully observed output functions and the other for partially observed ones. Both are backed theoretically by an excess risk analysis. Then, in the more general setting of integral losses based on differentiable ground losses, KPL is implemented using first-order optimization for both fully and partially observed output functions. Eventually, several robustness aspects of the proposed algorithms are highlighted on a toy dataset; and a study on two real datasets shows that they are competitive compared to other nonlinear approaches while keeping the computational cost significantly lower.