This review provides an overview of data-driven model predictive control (MPC) methods for controlling unknown systems, focusing on systems-theoretic guarantees such as stability, robustness, and constraint satisfaction. The methods rely on the Fundamental Lemma from behavioral theory to predict input-output trajectories directly from data. The review covers various setups, including linear systems with noise-free data and more realistic formulations with noise and nonlinearities. It discusses different techniques to ensure closed-loop system guarantees and highlights future research avenues to improve theoretical understanding and practical applicability of data-driven MPC. The review is structured into sections on preliminaries, data-driven MPC for linear systems, robust data-driven MPC for noisy data, and data-driven MPC for nonlinear systems. Key topics include the Fundamental Lemma, model-based MPC, data-driven MPC with noise-free and noisy data, and advanced control objectives. The review also explores the use of regularization in data-driven MPC and the application of stochastic methods for handling disturbances.This review provides an overview of data-driven model predictive control (MPC) methods for controlling unknown systems, focusing on systems-theoretic guarantees such as stability, robustness, and constraint satisfaction. The methods rely on the Fundamental Lemma from behavioral theory to predict input-output trajectories directly from data. The review covers various setups, including linear systems with noise-free data and more realistic formulations with noise and nonlinearities. It discusses different techniques to ensure closed-loop system guarantees and highlights future research avenues to improve theoretical understanding and practical applicability of data-driven MPC. The review is structured into sections on preliminaries, data-driven MPC for linear systems, robust data-driven MPC for noisy data, and data-driven MPC for nonlinear systems. Key topics include the Fundamental Lemma, model-based MPC, data-driven MPC with noise-free and noisy data, and advanced control objectives. The review also explores the use of regularization in data-driven MPC and the application of stochastic methods for handling disturbances.