Substellar science in the wake of the ESA Euclid space mission

The ESA space mission Euclid was launched on July 1st, 2023 and is undergoing its science verification phase. In this invited review we show that Euclid means a before and an after for our understanding of ultra-cool dwarfs and substellar-mass objects and their connections with stars, exoplanets and the Milky Way. Euclid enables the study with unprecedented statistical significance a very large ensemble of ultracool dwarfs, the identification of new types of substellar objects, and the determination of the substellar binary fraction and the Initial Mass Function (IMF) in diverse galactic environments from the nearest stellar nurseries to the ancient relics of Galactic formation.