<p>The scheduling of flow shops with multiple dedicated machines, a problem referred to in the literature under various names such as Hybrid Flow Shop with Dedicated Machines (HFSDM), Flow Shop with Parallel Dedicated Machines, Differentiation Flow Shop, or Flow Shop with a Critical Machine, presents a complex optimization challenge encountered in many real-life applications. Given its strong relevance in both theory and practice, this problem has attracted considerable attention in the literature. This growing interest underlines the need for a more detailed and structured analysis, which this paper aims to provide. We begin by examining the main theoretical aspects of the HFSDM problem, with a particular focus on its structural characteristics and computational complexity, in order to build a clear foundation for the study. We then propose a classification of existing works according to the solution approaches adopted, allowing for a more organized and readable overview of the field. It succinctly explores and examines several configurations of the HFSDM scheduling problem, each addressing distinct constraints, assumptions, and optimality criteria. The paper concludes by identifying emerging research opportunities and suggesting promising directions for future work in the field of Hybrid Flow Shop with Dedicated Machines.</p>