Based on the contextualization of the current problem of the worldwide oil refining industry and the need to transform heavy crude to medium distillates, gasoline and diesel, this chapter highlights the use of hydrocracking as a versatile and flexible process for the treatment of this type of crude. Herein we describe the main characteristics and challenges (deactivation due to contaminants or coke formation, control of molecular traffic and acid modulation) that a catalyst must face for its good performance in this reaction. A review of the most reported catalysts for hydrocracking processes points to zeolites and, to a lesser extent, to silica-alumina as the main solids used and highlights the lesser attention that has been given to other materials such as clay minerals that, by their very nature, offer potential interest, particularly in the context of current environmental needs and restrictions. Within this context, the fundamental characteristics of natural clay minerals are set forth, emphasizing the main methodologies used to modify them and highlighting the potential they offer as supports and as a source of acid sites for the conformation of new, potentially efficient and competitive catalysts for hydrocracking processes.