Smart manufacturing implies creating virtual replicas of the processing operations, taking into account the material dimension and its multi-physics transformation when forming processes operate. Performing efficient, that is, online accurate predictions of the induced properties (including potential defects) of the formed part (to optimally control the process parameters) needs moving beyond usual offline simulation based on nominal models, and proceeds by assimilating data. This will serve, from one side, to keep the model calibrated, and from the other, to enrich the model and its associated predictions, to avoid bias, to improve accuracy or for performing online diagnosis, by advertising on preventive maintenance. For all these purposes, a new alliance between physics-based and data-driven modelling approaches seems a very valuable route for empowering engineering in general, and smart manufacturing in particular. The present paper revisits the main methodologies involved in the construction of the component or system Hybrid Twins.