Meal delivery services have undergone a tremendous evolution during the last decade and, according to market predictions, this trend will continue to grow in the following years. The service growth forecast in combination with the high complexity of the problem indicate the importance of achieving efficient solutions. This article presents a detailed description of the meal delivery problem (MDP) as well as the main research directions appearing in the existing literature. The characteristics that increase the complexity of the problem are highlighted, namely, the dynamic nature of the delivery tasks; the tight delivery time requirements; and the interdependencies among stakeholders, which are connected by nonexclusive relationships. Open challenges of the problem are analyzed, including the expected future shift toward autonomous deliveries as well as other general future directions.