Digital twins are fast becoming an essential technology for decision-making at every level in the industry in the face of uncertainty, competition, and rapid developments in technology. The increasing modeling complexity can hinder rapid, verifiable decision-making, which we seek to address using what we refer to as control-oriented digital twins. Control-oriented digital twins are created by applying model order reduction techniques and multi-modeling approaches to full-scale models. The purpose of this chapter is to review the principles underlying model order reduction and multi-modeling. These techniques are illustrated through two case studies, one based on a chemical industrial plant and one based on a social system.