What is a good local description of contact dynamics for contact-rich manipulation, and where can we trust this local description? While many approaches often rely on the Taylor approximation of dynamics with an ellipsoidal trust region, we argue that such approaches are fundamentally inconsistent with the unilateral nature of contact. As a remedy, we present the Contact Trust Region (CTR), which captures the unilateral nature of contact while remaining efficient for computation. With CTR, we first develop a Model-Predictive Control (MPC) algorithm capable of synthesizing local contact-rich plans. Then, we extend this capability to plan globally by stitching together local MPC plans, enabling efficient and dexterous contact-rich manipulation. To verify the performance of our method, we perform comprehensive evaluations, both in high-fidelity simulation and on hardware, on two contact-rich systems: a planar IiwaBimanual system and a 3D AllegroHand system. On both systems, our method offers a significantly lower-compute alternative to existing RL-based approaches to contact-rich manipulation. In particular, our Allegro in-hand manipulation policy, in the form of a roadmap, takes fewer than 10 minutes to build offline on a standard laptop using just its CPU, with online inference taking just a few seconds. Experiment data, video and code are available at ctr.theaiinstitute.com.