The process of finding new materials, optimal for a given application, is lengthy, often unpredictable, and has a low throughput. Here I will describe a collection of numerical methods, merging advanced electronic structure theory and machine learning, for the discovery of novel compounds, which demonstrates an unprecedented throughput and discovery speed. This is applied here to magnetism, but it can be used for any materials class and potential application. Firstly, I will discuss a machine-learning scheme for predicting the Curie temperature of ferromagnets, which uses solely the chemical composition of a compound as feature and experimental data as target. In particular, I will discuss how to develop meaningful feature attributes for magnetism and how these can be informed by experimental and theoretical results. Then, I will describe how an accurate description of the structure of materials, which is amenable to be used with machine learning, can offer a quantum-chemistry-accurate description of local properties at virtually no computational costs. The method is not just suitable for building energy models, namely force fields to used across a broad spectrum of conditions, but also for any other local electronic quantity. These models may then be employed to design new materials, as demonstrated here for magnetic molecules with enhanced uniaxial anisotropy. Finally, I will present a novel rotationally invariant representation for generic vector fields. This can be used to generate linear and non-linear machine-learning models, where the total energy depends both on the atomic position and the vector field direction5. The scheme will be put to the test against a hierarchy of simple spin models, demonstrating an impressive ability to extrapolate away from the training region of the data. Application to complex potential energy surfaces, as those extracted from DFT are then envisioned.