This review provides an overview of data-driven model predictive control (MPC) with systems-theoretic guarantees for controlling unknown systems. The paper discusses data-driven MPC methods that rely on the Fundamental Lemma from behavioral theory to predict input-output trajectories directly from data. It covers various setups, including linear and nonlinear systems, as well as noise-free and noisy data, and provides an overview of techniques to ensure guarantees for the closed-loop system. The review highlights the importance of theoretical guarantees for reliable operation in real-world applications, especially for complex and safety-critical systems. It discusses different approaches to ensure stability, robustness, and constraint satisfaction, including terminal ingredients, regularization, and robustification techniques. The paper also addresses the challenges of applying data-driven MPC to nonlinear systems and presents alternative approaches such as exploiting global linearity or using adaptive data updates. The review concludes with a discussion of future research directions in data-driven MPC, emphasizing the need for further theoretical understanding and practical applicability.This review provides an overview of data-driven model predictive control (MPC) with systems-theoretic guarantees for controlling unknown systems. The paper discusses data-driven MPC methods that rely on the Fundamental Lemma from behavioral theory to predict input-output trajectories directly from data. It covers various setups, including linear and nonlinear systems, as well as noise-free and noisy data, and provides an overview of techniques to ensure guarantees for the closed-loop system. The review highlights the importance of theoretical guarantees for reliable operation in real-world applications, especially for complex and safety-critical systems. It discusses different approaches to ensure stability, robustness, and constraint satisfaction, including terminal ingredients, regularization, and robustification techniques. The paper also addresses the challenges of applying data-driven MPC to nonlinear systems and presents alternative approaches such as exploiting global linearity or using adaptive data updates. The review concludes with a discussion of future research directions in data-driven MPC, emphasizing the need for further theoretical understanding and practical applicability.