The main concern of the manufacturing industry is maintaining the tools of production so that they are in good working order. However, the maintenance and production functions are linked because the integrated management of these two functions is necessary for the efficient operation of the means of production. In fact, when the demand exceeds the maximum production capacity, the company takes on subcontracting to meet the needs of the customers. The objective of this research is to identify the current and future direction of research in this field according to the different classification criteria proposed. In this paper, firstly, the different approaches of maintenance integrated into production systems are presented. Secondly, the models that deal with joint maintenance management and subcontracting production as a solution that aligns with the company's strategic objectives are discussed as well as the resolution and management approaches that integrated problem optimisation. Finally, a comparative study of existing approaches was conducted and their purpose analysed. As perspective, we will propose and implement in our future research a model and powerful tool to establish a better policy of maintenance integrated to the production using subcontracting.